Science.gov

Sample records for input negative entropy

  1. Negative Entropy of Life

    NASA Astrophysics Data System (ADS)

    Goradia, Shantilal

    2015-10-01

    We modify Newtonian gravity to probabilistic quantum mechanical gravity to derive strong coupling. If this approach is valid, we should be able to extend it to the physical body (life) as follows. Using Boltzmann equation, we get the entropy of the universe (137) as if its reciprocal, the fine structure constant (ALPHA), is the hidden candidate representing the negative entropy of the universe which is indicative of the binary information as its basis (http://www.arXiv.org/pdf/physics0210040v5). Since ALPHA relates to cosmology, it must relate to molecular biology too, with the binary system as the fundamental source of information for the nucleotides of the DNA as implicit in the book by the author: ``Quantum Consciousness - The Road to Reality.'' We debate claims of anthropic principle based on the negligible variation of ALPHA and throw light on thermodynamics. We question constancy of G in multiple ways.

  2. Negative temperatures and the definition of entropy

    NASA Astrophysics Data System (ADS)

    Swendsen, Robert H.; Wang, Jian-Sheng

    2016-07-01

    The concept of negative temperature has recently received renewed interest in the context of debates about the correct definition of the thermodynamic entropy in statistical mechanics. Several researchers have identified the thermodynamic entropy exclusively with the "volume entropy" suggested by Gibbs, and have further concluded that by this definition, negative temperatures violate the principles of thermodynamics. We disagree with these conclusions. We demonstrate that volume entropy is inconsistent with the postulates of thermodynamics for systems with non-monotonic energy densities, while a definition of entropy based on the probability distributions of macroscopic variables does satisfy the postulates of thermodynamics. Our results confirm that negative temperature is a valid extension of thermodynamics.

  3. Correlation entropy of synaptic input-output dynamics

    NASA Astrophysics Data System (ADS)

    Kleppe, Ingo C.; Robinson, Hugh P. C.

    2006-10-01

    The responses of synapses in the neocortex show highly stochastic and nonlinear behavior. The microscopic dynamics underlying this behavior, and its computational consequences during natural patterns of synaptic input, are not explained by conventional macroscopic models of deterministic ensemble mean dynamics. Here, we introduce the correlation entropy of the synaptic input-output map as a measure of synaptic reliability which explicitly includes the microscopic dynamics. Applying this to experimental data, we find that cortical synapses show a low-dimensional chaos driven by the natural input pattern.

  4. Connectivity in the human brain dissociates entropy and complexity of auditory inputs.

    PubMed

    Nastase, Samuel A; Iacovella, Vittorio; Davis, Ben; Hasson, Uri

    2015-03-01

    Complex systems are described according to two central dimensions: (a) the randomness of their output, quantified via entropy; and (b) their complexity, which reflects the organization of a system's generators. Whereas some approaches hold that complexity can be reduced to uncertainty or entropy, an axiom of complexity science is that signals with very high or very low entropy are generated by relatively non-complex systems, while complex systems typically generate outputs with entropy peaking between these two extremes. In understanding their environment, individuals would benefit from coding for both input entropy and complexity; entropy indexes uncertainty and can inform probabilistic coding strategies, whereas complexity reflects a concise and abstract representation of the underlying environmental configuration, which can serve independent purposes, e.g., as a template for generalization and rapid comparisons between environments. Using functional neuroimaging, we demonstrate that, in response to passively processed auditory inputs, functional integration patterns in the human brain track both the entropy and complexity of the auditory signal. Connectivity between several brain regions scaled monotonically with input entropy, suggesting sensitivity to uncertainty, whereas connectivity between other regions tracked entropy in a convex manner consistent with sensitivity to input complexity. These findings suggest that the human brain simultaneously tracks the uncertainty of sensory data and effectively models their environmental generators.

  5. Configurational Information as Potentially Negative Entropy: The Triple Helix Model

    NASA Astrophysics Data System (ADS)

    Leydesdorff, Loet

    2008-12-01

    Configurational information is generated when three or more sources of variance interact. The variations not only disturb each other relationally, but by selecting upon each other, they are also positioned in a configuration. A configuration can be stabilized and/or globalized. Different stabilizations can be considered as second-order variation, and globalization as a second-order selection. The positive manifestations and the negative selections operate upon one another by adding and reducing uncertainty, respectively. Reduction of uncertainty in a configuration can be measured in bits of information. The variables can also be considered as dimensions of the probabilistic entropy in the system(s) under study. The configurational information then provides us with a measure of synergy within a complex system. For example, the knowledge base of an economy can be considered as such a synergy in the otherwise virtual (that is, fourth) dimension of a regime

  6. The Stumbling Block of the Gibbs Entropy: the Reality of the Negative Absolute Temperatures

    NASA Astrophysics Data System (ADS)

    Anghel, Dragoş-Victor

    2016-02-01

    The second Tisza-Callen postulate of equilibrium thermodynamics states that for any system there exists a function of the system extensive parameters, called entropy, defined for all equilibrium states and having the property that the values assumed by the extensive parameters in the absence of a constraint are those that maximize the entropy over the manifold of constrained equilibrium states. Based on the thermodynamic evolution of systems which (in the Boltzmann description) have positive and negative temperatures, we show that this postulate is satisfied by the Boltzmann formula for the entropy and may be violated by the Gibbs formula, therefore invalidating the later. Vice versa, if we assume, by reductio ad absurdum, that for some thermodynamic systems the equilibrium state is determined by the Gibbs' prescription and not by Boltzmann's, this implies that such systems have macroscopic fluctuations and therefore do not reach the thermodynamic equilibrium.

  7. Entropies of negative incomes, Pareto-distributed loss, and financial crises.

    PubMed

    Gao, Jianbo; Hu, Jing; Mao, Xiang; Zhou, Mi; Gurbaxani, Brian; Lin, Johnny

    2011-01-01

    Health monitoring of world economy is an important issue, especially in a time of profound economic difficulty world-wide. The most important aspect of health monitoring is to accurately predict economic downturns. To gain insights into how economic crises develop, we present two metrics, positive and negative income entropy and distribution analysis, to analyze the collective "spatial" and temporal dynamics of companies in nine sectors of the world economy over a 19 year period from 1990-2008. These metrics provide accurate predictive skill with a very low false-positive rate in predicting downturns. The new metrics also provide evidence of phase transition-like behavior prior to the onset of recessions. Such a transition occurs when negative pretax incomes prior to or during economic recessions transition from a thin-tailed exponential distribution to the higher entropy Pareto distribution, and develop even heavier tails than those of the positive pretax incomes. These features propagate from the crisis initiating sector of the economy to other sectors.

  8. Exact master equation for a spin interacting with a spin bath: Non-Markovianity and negative entropy production rate

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Samyadeb; Misra, Avijit; Mukhopadhyay, Chiranjib; Pati, Arun Kumar

    2017-01-01

    An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the dynamics in terms of the divisibility breaking of the dynamical map and the increase of the trace distance fidelity between quantum states is shown. Moreover, it is observed that the irreversible entropy production rate is always negative (for a fixed initial state) whenever the dynamics exhibits non-Markovian behavior. In continuation with the study of witnessing non-Markovianity, it is shown that the positive rate of change of the purity of the central qubit is a faithful indicator of the non-Markovian information backflow. Given the experimental feasibility of measuring the purity of a quantum state, a possibility of experimental demonstration of non-Markovianity and the negative irreversible entropy production rate is addressed. This gives the present work considerable practical importance for detecting the non-Markovianity and the negative irreversible entropy production rate.

  9. Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis

    PubMed Central

    Dordek, Yedidyah; Soudry, Daniel; Meir, Ron; Derdikman, Dori

    2016-01-01

    Many recent models study the downstream projection from grid cells to place cells, while recent data have pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the place cells. We propose a single-layer neural network with feedforward weights connecting place-like input cells to grid cell outputs. Place-to-grid weights are learned via a generalized Hebbian rule. The architecture of this network highly resembles neural networks used to perform Principal Component Analysis (PCA). Both numerical results and analytic considerations indicate that if the components of the feedforward neural network are non-negative, the output converges to a hexagonal lattice. Without the non-negativity constraint, the output converges to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules is −1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA. DOI: http://dx.doi.org/10.7554/eLife.10094.001 PMID:26952211

  10. Negative auto-regulation increases the input dynamic-range of the arabinose system of Escherichia coli

    PubMed Central

    2011-01-01

    Background Gene regulation networks are made of recurring regulatory patterns, called network motifs. One of the most common network motifs is negative auto-regulation, in which a transcription factor represses its own production. Negative auto-regulation has several potential functions: it can shorten the response time (time to reach halfway to steady-state), stabilize expression against noise, and linearize the gene's input-output response curve. This latter function of negative auto-regulation, which increases the range of input signals over which downstream genes respond, has been studied by theory and synthetic gene circuits. Here we ask whether negative auto-regulation preserves this function also in the context of a natural system, where it is embedded within many additional interactions. To address this, we studied the negative auto-regulation motif in the arabinose utilization system of Escherichia coli, in which negative auto-regulation is part of a complex regulatory network. Results We find that when negative auto-regulation is disrupted by placing the regulator araC under constitutive expression, the input dynamic range of the arabinose system is reduced by 10-fold. The apparent Hill coefficient of the induction curve changes from about n = 1 with negative auto-regulation, to about n = 2 when it is disrupted. We present a mathematical model that describes how negative auto-regulation can increase input dynamic-range, by coupling the transcription factor protein level to the input signal. Conclusions Here we demonstrate that the negative auto-regulation motif in the native arabinose system of Escherichia coli increases the range of arabinose signals over which the system can respond. In this way, negative auto-regulation may help to increase the input dynamic-range while maintaining the specificity of cooperative regulatory systems. This function may contribute to explaining the common occurrence of negative auto-regulation in biological systems. PMID

  11. Edge theory approach to topological entanglement entropy, mutual information, and entanglement negativity in Chern-Simons theories

    NASA Astrophysics Data System (ADS)

    Wen, Xueda; Matsuura, Shunji; Ryu, Shinsei

    2016-06-01

    We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our approach is complementary to, e.g., the existing methods using replica trick and Witten's method of surgery, and applies to a generic spatial manifold of genus g , which can be bipartitioned in an arbitrary way. The effects of fusion and braiding of Wilson lines can be also straightforwardly studied within our framework. By considering a generic superposition of states with different Wilson line configurations, through an interference effect, we can detect, by the entanglement entropy, the topological data of Chern-Simons theories, e.g., the R symbols, monodromy, and topological spins of quasiparticles. Furthermore, by using our method, we calculate other entanglement/correlation measures such as the mutual information and the entanglement negativity. In particular, it is found that the entanglement negativity of two adjacent noncontractible regions on a torus provides a simple way to distinguish Abelian and non-Abelian topological orders.

  12. Comment on "Carbon-negative biofuels from low-input high-diversity grassland biomass".

    PubMed

    Russelle, Michael P; Morey, R Vance; Baker, John M; Porter, Paul M; Jung, Hans-Joachim G

    2007-06-15

    Tilman et al. (Reports, 8 December 2006, p. 1598) argued that low-input high-diversity grasslands can provide a substantial proportion of global energy needs. We contend that their conclusions are not substantiated by their experimental protocol. The authors understated the management inputs required to establish prairies, extrapolated globally from site-specific results, and presented potentially misleading energy accounting.

  13. Coexistence of positive and negative magnetic entropy changes in CeMn2(Si1 - xGex)2 compounds

    NASA Astrophysics Data System (ADS)

    Zuo, Wen-Liang; Hu, Feng-Xia; Sun, Ji-Rong; Shen, Bao-Gen

    2015-09-01

    A series of CeMn2(Si1-xGex)2 (x = 0.2, 0.4, 0.6, 0.8) compounds are prepared by the arc-melting method. All the samples primarily crystallize in the ThCr2Si2-type structure. The temperature dependences of zero-field-cooled (ZFC) and FC magnetization measurements show a transition from antiferromagnetic (AFM) state to ferromagnetic (FM) state at room temperature with the increase of the Ge concentration. For x = 0.4, the sample exhibits two kinds of phase transitions with increasing temperature: from AFM to FM and from FM to paramagnetic (PM) at around TN ˜ 197 K and TC ˜ 300 K, respectively. The corresponding Arrott curves indicate that the AFM-FM transition is of first-order character and the FM-PM transition is of second-order character. Meanwhile, the coexistence of positive and negative magnetic entropy changes can be observed, which are corresponding to the AFM-FM and FM-PM transitions, respectively. Project supported by the Beijing Natural Science Foundation, China (Grant No. 2152034) and the National Natural Science Foundation of China (Grant Nos. 11274357 and 51271196).

  14. Seeking the foundations of cognition in bacteria: From Schrödinger's negative entropy to latent information

    NASA Astrophysics Data System (ADS)

    Ben Jacob, Eshel; Shapira, Yoash; Tauber, Alfred I.

    2006-01-01

    We reexamine Schrödinger's reflections on the fundamental requirements for life in view of new observations about bacterial self-organization and the emerging understanding of gene-network regulation mechanisms and dynamics. Focusing on the energy, matter and thermodynamic imbalances provided by the environment, Schrödinger proposed his consumption of negative entropy requirement for life. We take the criteria further and propose that, besides “negative entropy”, organisms extract latent information embedded in the complexity of their environment. By latent information we refer to the non-arbitrary spatio-temporal patterns of regularities and variations that characterize the environmental dynamics. Hence it can be used to generate an internal condensed description (model or usable information) of the environment which guides the organisms functioning. Accordingly, we propose that Schrödinger's criterion of “consumption of negative entropy” is not sufficient and “consumption of latent information” is an additional fundamental requirement of Life. In other words, all organisms, including bacteria, the most primitive (fundamental) ones, must be able to sense the environment and perform internal information processing for thriving on latent information embedded in the complexity of their environment. We then propose that by acting together, bacteria can perform this most elementary cognitive function more efficiently as can be illustrated by their cooperative behavior (colonial or inter-cellular self-organization). As a member of a complex superorganism-the colony-each unit (bacteria) must possess the ability to sense and communicate with the other units comprising the collective and perform its task within a distribution of tasks. Bacterial communication thus entails collective sensing and cooperativity. The fundamental (primitive) elements of cognition in such systems include interpretation of (chemical) messages, distinction between internal and

  15. Coherent Behavior and the Bound State of Water and K(+) Imply Another Model of Bioenergetics: Negative Entropy Instead of High-energy Bonds.

    PubMed

    Jaeken, Laurent; Vasilievich Matveev, Vladimir

    2012-01-01

    Observations of coherent cellular behavior cannot be integrated into widely accepted membrane (pump) theory (MT) and its steady state energetics because of the thermal noise of assumed ordinary cell water and freely soluble cytoplasmic K(+). However, Ling disproved MT and proposed an alternative based on coherence, showing that rest (R) and action (A) are two different phases of protoplasm with different energy levels. The R-state is a coherent metastable low-entropy state as water and K(+) are bound to unfolded proteins. The A-state is the higher-entropy state because water and K(+) are free. The R-to-A phase transition is regarded as a mechanism to release energy for biological work, replacing the classical concept of high-energy bonds. Subsequent inactivation during the endergonic A-to-R phase transition needs an input of metabolic energy to restore the low entropy R-state. Matveev's native aggregation hypothesis allows to integrate the energetic details of globular proteins into this view.

  16. Coherent Behavior and the Bound State of Water and K+ Imply Another Model of Bioenergetics: Negative Entropy Instead of High-energy Bonds

    PubMed Central

    Jaeken, Laurent; Vasilievich Matveev, Vladimir

    2012-01-01

    Observations of coherent cellular behavior cannot be integrated into widely accepted membrane (pump) theory (MT) and its steady state energetics because of the thermal noise of assumed ordinary cell water and freely soluble cytoplasmic K+. However, Ling disproved MT and proposed an alternative based on coherence, showing that rest (R) and action (A) are two different phases of protoplasm with different energy levels. The R-state is a coherent metastable low-entropy state as water and K+ are bound to unfolded proteins. The A-state is the higher-entropy state because water and K+ are free. The R-to-A phase transition is regarded as a mechanism to release energy for biological work, replacing the classical concept of high-energy bonds. Subsequent inactivation during the endergonic A-to-R phase transition needs an input of metabolic energy to restore the low entropy R-state. Matveev’s native aggregation hypothesis allows to integrate the energetic details of globular proteins into this view. PMID:23264833

  17. Parole release decisions: impact of positive and negative victim and nonvictim input on a representative sample of parole-eligible inmates.

    PubMed

    Caplan, Joel M

    2010-01-01

    This study analyzed administrative data from the New Jersey State Parole Board to determine the extent to which victim and nonvictim input impacted parole release decisions. Positive and negative input, in both verbal and written forms, was studied for a representative sample of 820 parole-eligible adult inmates. Victim input was not found to be a significant predictor of parole release; measures of institutional behavior, crime severity, and criminal history were significant. Though insignificant, verbal input had a greater effect than written input. Results suggest that the impact of victim input is not generalizable across different types of offenders or across different paroling jurisdictions. It can no longer be assumed that victim rights laws and public participation at parole guarantee victim-desired outcomes.

  18. Specification of motoneuron fate in Drosophila: integration of positive and negative transcription factor inputs by a minimal eve enhancer.

    PubMed

    McDonald, Jocelyn A; Fujioka, Miki; Odden, Joanne P; Jaynes, James B; Doe, Chris Q

    2003-11-01

    We are interested in the mechanisms that generate neuronal diversity within the Drosophila central nervous system (CNS), and in particular in the development of a single identified motoneuron called RP2. Expression of the homeodomain transcription factor Even-skipped (Eve) is required for RP2 to establish proper connectivity with its muscle target. Here we investigate the mechanisms by which eve is specifically expressed within the RP2 motoneuron lineage. Within the NB4-2 lineage, expression of eve first occurs in the precursor of RP2, called GMC4-2a. We identify a small 500 base pair eve enhancer that mediates eve expression in GMC4-2a. We show that four different transcription factors (Prospero, Huckebein, Fushi tarazu, and Pdm1) are all expressed in GMC4-2a, and are required to activate eve via this minimal enhancer, and that one transcription factor (Klumpfuss) represses eve expression via this element. All four positively acting transcription factors act independently, regulating eve but not each other. Thus, the eve enhancer integrates multiple positive and negative transcription factor inputs to restrict eve expression to a single precursor cell (GMC4-2a) and its RP2 motoneuron progeny.

  19. A Regulated Double-Negative Feedback Decodes the Temporal Gradient of Input Stimulation in a Cell Signaling Network

    PubMed Central

    Park, Sang-Min; Shin, Sung-Young; Cho, Kwang-Hyun

    2016-01-01

    Revealing the hidden mechanism of how cells sense and react to environmental signals has been a central question in cell biology. We focused on the rate of increase of stimulation, or temporal gradient, known to cause different responses of cells. We have investigated all possible three-node enzymatic networks and identified a network motif that robustly generates a transient or sustained response by acute or gradual stimulation, respectively. We also found that a regulated double-negative feedback within the motif is essential for the temporal gradient-sensitive switching. Our analysis highlights the essential structure and mechanism enabling cells to properly respond to dynamic environmental changes. PMID:27584002

  20. Entropy, materials, and posterity

    USGS Publications Warehouse

    Cloud, P.

    1977-01-01

    Materials and energy are the interdependent feedstocks of economic systems, and thermodynamics is their moderator. It costs energy to transform the dispersed minerals of Earth's crust into ordered materials and structures. And it costs materials to collect and focus the energy to perform work - be it from solar, fossil fuel, nuclear, or other sources. The greater the dispersal of minerals sought, the more energy is required to collect them into ordered states. But available energy can be used once only. And the ordered materials of industrial economies become disordered with time. They may be partially reordered and recycled, but only at further costs in energy. Available energy everywhere degrades to bound states and order to disorder - for though entropy may be juggled it always increases. Yet industry is utterly dependent on low entropy states of matter and energy, while decreasing grades of ore require ever higher inputs of energy to convert them to metals, with ever increasing growth both of entropy and environmental hazard. Except as we may prize a thing for its intrinsic qualities - beauty, leisure, love, or gold - low-entropy is the only thing of real value. It is worth whatever the market will bear, and it becomes more valuable as entropy increases. It would be foolish of suppliers to sell it more cheaply or in larger amounts than their own enjoyment of life requires, whatever form it may take. For this reason, and because of physical constraints on the availability of all low-entropy states, the recent energy crises is only the first of a sequence of crises to be expected in energy and materials as long as current trends continue. The apportioning of low-entropy states in a modern industrial society is achieved more or less according to the theory of competitive markets. But the rational powers of this theory suffer as the world grows increasingly polarized into rich, over-industrialized nations with diminishing resource bases and poor, supplier nations

  1. Expression of the Troponin C at 41C Gene in Adult Drosophila Tubular Muscles Depends upon Both Positive and Negative Regulatory Inputs.

    PubMed

    Chechenova, Maria B; Maes, Sara; Cripps, Richard M

    2015-01-01

    Most animals express multiple isoforms of structural muscle proteins to produce tissues with different physiological properties. In Drosophila, the adult muscles include tubular-type muscles and the fibrillar indirect flight muscles. Regulatory processes specifying tubular muscle fate remain incompletely understood, therefore we chose to analyze the transcriptional regulation of TpnC41C, a Troponin C gene expressed in the tubular jump muscles, but not in the fibrillar flight muscles. We identified a 300-bp promoter fragment of TpnC41C sufficient for the fiber-specific reporter expression. Through an analysis of this regulatory element, we identified two sites necessary for the activation of the enhancer. Mutations in each of these sites resulted in 70% reduction of enhancer activity. One site was characterized as a binding site for Myocyte Enhancer Factor-2. In addition, we identified a repressive element that prevents activation of the enhancer in other muscle fiber types. Mutation of this site increased jump muscle-specific expression of the reporter, but more importantly reporter expression expanded into the indirect flight muscles. Our findings demonstrate that expression of the TpnC41C gene in jump muscles requires integration of multiple positive and negative transcriptional inputs. Identification of the transcriptional regulators binding the cis-elements that we identified will reveal the regulatory pathways controlling muscle fiber differentiation.

  2. Entropy and Enzyme Catalysis.

    PubMed

    Åqvist, Johan; Kazemi, Masoud; Isaksen, Geir Villy; Brandsdal, Bjørn Olav

    2017-02-21

    The role played by entropy for the enormous rate enhancement achieved by enzymes has been debated for many decades. There are, for example, several confirmed cases where the activation free energy is reduced by around 10 kcal/mol due to entropic effects, corresponding to a rate enhancement of ∼10(7) compared to the uncatalyzed reaction. However, despite substantial efforts from both the experimental and theoretical side, no real consensus has been reached regarding the origin of such large entropic contributions to enzyme catalysis. Another remarkable instance of entropic effects is found in enzymes that are adapted by evolution to work at low temperatures, near the freezing point of water. These cold-adapted enzymes invariably show a more negative entropy and a lower enthalpy of activation than their mesophilic orthologs, which counteracts the exponential damping of reaction rates at lower temperature. The structural origin of this universal phenomenon has, however, remained elusive. The basic problem with connecting macroscopic thermodynamic quantities, such as activation entropy and enthalpy derived from Arrhenius plots, to the 3D protein structure is that the underlying detailed (microscopic) energetics is essentially inaccessible to experiment. Moreover, attempts to calculate entropy contributions by computer simulations have mostly focused only on substrate entropies, which do not provide the full picture. We have recently devised a new approach for accessing thermodynamic activation parameters of both enzyme and solution reactions from computer simulations, which turns out to be very successful. This method is analogous to the experimental Arrhenius plots and directly evaluates the temperature dependence of calculated reaction free energy profiles. Hence, by extensive molecular dynamics simulations and calculations of up to thousands of independent free energy profiles, we are able to extract activation parameters with sufficient precision for making

  3. Upper entropy axioms and lower entropy axioms

    SciTech Connect

    Guo, Jin-Li Suo, Qi

    2015-04-15

    The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics.

  4. Maximum Entropy Guide for BSS

    NASA Astrophysics Data System (ADS)

    Górriz, J. M.; Puntonet, C. G.; Medialdea, E. G.; Rojas, F.

    2005-11-01

    This paper proposes a novel method for Blindly Separating unobservable independent component (IC) Signals (BSS) based on the use of a maximum entropy guide (MEG). The paper also includes a formal proof on the convergence of the proposed algorithm using the guiding operator, a new concept in the genetic algorithm (GA) scenario. The Guiding GA (GGA) presented in this work, is able to extract IC with faster rate than the previous ICA algorithms, based on maximum entropy contrast functions, as input space dimension increases. It shows significant accuracy and robustness than the previous approaches in any case.

  5. On the dispute between Boltzmann and Gibbs entropy

    NASA Astrophysics Data System (ADS)

    Buonsante, Pierfrancesco; Franzosi, Roberto; Smerzi, Augusto

    2016-12-01

    The validity of the concept of negative temperature has been recently challenged by arguing that the Boltzmann entropy (that allows negative temperatures) is inconsistent from a mathematical and statistical point of view, whereas the Gibbs entropy (that does not admit negative temperatures) provides the correct definition for the microcanonical entropy. Here we prove that the Boltzmann entropy is thermodynamically and mathematically consistent. Analytical results on two systems supporting negative temperatures illustrate the scenario we propose. In addition we numerically study a lattice system to show that negative temperature equilibrium states are accessible and obey standard statistical mechanics prediction.

  6. In defense of negative temperature

    NASA Astrophysics Data System (ADS)

    Poulter, J.

    2016-03-01

    This pedagogical comment highlights three misconceptions concerning the usefulness of the concept of negative temperature, being derived from the usual, often termed Boltzmann, definition of entropy. First, both the Boltzmann and Gibbs entropies must obey the same thermodynamic consistency relation. Second, the Boltzmann entropy does obey the second law of thermodynamics. Third, there exists an integrating factor of the heat differential with both definitions of entropy.

  7. Entropy power inequalities for qudits

    NASA Astrophysics Data System (ADS)

    Audenaert, Koenraad; Datta, Nilanjana; Ozols, Maris

    2016-05-01

    Shannon's entropy power inequality (EPI) can be viewed as a statement of concavity of an entropic function of a continuous random variable under a scaled addition rule: f ( √{ a } X + √{ 1 - a } Y ) ≥ a f ( X ) + ( 1 - a ) f ( Y ) ∀ a ∈ [ 0 , 1 ] . Here, X and Y are continuous random variables and the function f is either the differential entropy or the entropy power. König and Smith [IEEE Trans. Inf. Theory 60(3), 1536-1548 (2014)] and De Palma, Mari, and Giovannetti [Nat. Photonics 8(12), 958-964 (2014)] obtained quantum analogues of these inequalities for continuous-variable quantum systems, where X and Y are replaced by bosonic fields and the addition rule is the action of a beam splitter with transmissivity a on those fields. In this paper, we similarly establish a class of EPI analogues for d-level quantum systems (i.e., qudits). The underlying addition rule for which these inequalities hold is given by a quantum channel that depends on the parameter a ∈ [0, 1] and acts like a finite-dimensional analogue of a beam splitter with transmissivity a, converting a two-qudit product state into a single qudit state. We refer to this channel as a partial swap channel because of the particular way its output interpolates between the states of the two qudits in the input as a is changed from zero to one. We obtain analogues of Shannon's EPI, not only for the von Neumann entropy and the entropy power for the output of such channels, but also for a much larger class of functions. This class includes the Rényi entropies and the subentropy. We also prove a qudit analogue of the entropy photon number inequality (EPnI). Finally, for the subclass of partial swap channels for which one of the qudit states in the input is fixed, our EPIs and EPnI yield lower bounds on the minimum output entropy and upper bounds on the Holevo capacity.

  8. The minimum entropy principle and task performance.

    PubMed

    Guastello, Stephen J; Gorin, Hillary; Huschen, Samuel; Peters, Natalie E; Fabisch, Megan; Poston, Kirsten; Weinberger, Kelsey

    2013-07-01

    According to the minimum entropy principle, efficient cognitive performance is produced with a neurocognitive strategy that involves a minimum of degrees of freedom. Although high performance is often regarded as consistent performance as well, some variability in performance still remains which allows the person to adapt to changing goal conditions or fatigue. The present study investigated the connection between performance, entropy in performance, and four task-switching strategies. Fifty-one undergraduates performed 7 different computer-based cognitive tasks producing sets of 49 responses under instructional conditions requiring task quotas or no quotas. The temporal patterns of performance were analyzed using orbital decomposition to extract pattern types and lengths, which were then compared with regard to Shannon entropy, topological entropy, and overall performance. Task switching strategies from a previous study were available for the same participants as well. Results indicated that both topological entropy and Shannon entropy were negatively correlated with performance. Some task-switching strategies produced lower entropy in performance than others. Stepwise regression showed that the top three predictors of performance were Shannon entropy and arithmetic and spatial abilities. Additional implications for the prediction of work performance with cognitive ability measurements and the applicability of the minimum entropy principle to multidimensional performance criteria and team work are discussed.

  9. Gravitational entropies in LTB dust models

    NASA Astrophysics Data System (ADS)

    Sussman, Roberto A.; Larena, Julien

    2014-04-01

    We consider generic Lemaître-Tolman-Bondi (LTB) dust models to probe the gravitational entropy proposals of Clifton, Ellis and Tavakol (CET) and of Hosoya and Buchert (HB). We also consider a variant of the HB proposal based on a suitable quasi-local scalar weighted average. We show that the conditions for entropy growth for all proposals are directly related to a negative correlation of similar fluctuations of the energy density and Hubble scalar. While this correlation is evaluated locally for the CET proposal, it must be evaluated in a non-local domain dependent manner for the two HB proposals. By looking at the fulfilment of these conditions at the relevant asymptotic limits we are able to provide a well grounded qualitative description of the full time evolution and radial asymptotic scaling of the three entropies in generic models. The following rigorous analytic results are obtained for the three proposals: (i) entropy grows when the density growing mode is dominant, (ii) all ever-expanding hyperbolic models reach a stable terminal equilibrium characterized by an inhomogeneous entropy maximum in their late time evolution; (iii) regions with decaying modes and collapsing elliptic models exhibit unstable equilibria associated with an entropy minimum (iv) near singularities the CET entropy diverges while the HB entropies converge; (v) the CET entropy converges for all models in the radial asymptotic range, whereas the HB entropies only converge for models asymptotic to a Friedmann-Lemaître-Robertson-Walker background. The fact that different independent proposals yield fairly similar conditions for entropy production, time evolution and radial scaling in generic LTB models seems to suggest that their common notion of a ‘gravitational entropy’ may be a theoretically robust concept applicable to more general spacetimes.

  10. Generalized entanglement entropy

    NASA Astrophysics Data System (ADS)

    Taylor, Marika

    2016-07-01

    We discuss two measures of entanglement in quantum field theory and their holographic realizations. For field theories admitting a global symmetry, we introduce a global symmetry entanglement entropy, associated with the partitioning of the symmetry group. This quantity is proposed to be related to the generalized holographic entanglement entropy defined via the partitioning of the internal space of the bulk geometry. Thesecond measure of quantum field theory entanglement is the field space entanglement entropy, obtained by integrating out a subset of the quantum fields. We argue that field space entanglement entropy cannot be precisely realised geometrically in a holographic dual. However, for holographic geometries with interior decoupling regions, the differential entropy provides a close analogue to the field space entanglement entropy. We derive generic descriptions of such inner throat regions in terms of gravity coupled to massive scalars and show how the differential entropy in the throat captures features of the field space entanglement entropy.

  11. Entropy, a Protean Concept

    NASA Astrophysics Data System (ADS)

    Balian, Roger

    We review at a tutorial level the many aspects of the concept of entropy and their interrelations, in thermodynamics, information theory, probability theory and statistical physics. The consideration of relevant entropies and the identification of entropy with missing information enlighten the paradoxes of irreversibility and of Maxwell's demon.

  12. Entropy Is Simple, Qualitatively.

    ERIC Educational Resources Information Center

    Lambert, Frank L.

    2002-01-01

    Suggests that qualitatively, entropy is simple. Entropy increase from a macro viewpoint is a measure of the dispersal of energy from localized to spread out at a temperature T. Fundamentally based on statistical and quantum mechanics, this approach is superior to the non-fundamental "disorder" as a descriptor of entropy change. (MM)

  13. Entropy: Order or Information

    ERIC Educational Resources Information Center

    Ben-Naim, Arieh

    2011-01-01

    Changes in entropy can "sometimes" be interpreted in terms of changes in disorder. On the other hand, changes in entropy can "always" be interpreted in terms of changes in Shannon's measure of information. Mixing and demixing processes are used to highlight the pitfalls in the association of entropy with disorder. (Contains 3 figures.)

  14. Modeling loop entropy.

    PubMed

    Chirikjian, Gregory S

    2011-01-01

    Proteins fold from a highly disordered state into a highly ordered one. Traditionally, the folding problem has been stated as one of predicting "the" tertiary structure from sequential information. However, new evidence suggests that the ensemble of unfolded forms may not be as disordered as once believed, and that the native form of many proteins may not be described by a single conformation, but rather an ensemble of its own. Quantifying the relative disorder in the folded and unfolded ensembles as an entropy difference may therefore shed light on the folding process. One issue that clouds discussions of "entropy" is that many different kinds of entropy can be defined: entropy associated with overall translational and rotational Brownian motion, configurational entropy, vibrational entropy, conformational entropy computed in internal or Cartesian coordinates (which can even be different from each other), conformational entropy computed on a lattice, each of the above with different solvation and solvent models, thermodynamic entropy measured experimentally, etc. The focus of this work is the conformational entropy of coil/loop regions in proteins. New mathematical modeling tools for the approximation of changes in conformational entropy during transition from unfolded to folded ensembles are introduced. In particular, models for computing lower and upper bounds on entropy for polymer models of polypeptide coils both with and without end constraints are presented. The methods reviewed here include kinematics (the mathematics of rigid-body motions), classical statistical mechanics, and information theory.

  15. RNA Thermodynamic Structural Entropy.

    PubMed

    Garcia-Martin, Juan Antonio; Clote, Peter

    2015-01-01

    Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http

  16. High Order Entropy-Constrained Residual VQ for Lossless Compression of Images

    NASA Technical Reports Server (NTRS)

    Kossentini, Faouzi; Smith, Mark J. T.; Scales, Allen

    1995-01-01

    High order entropy coding is a powerful technique for exploiting high order statistical dependencies. However, the exponentially high complexity associated with such a method often discourages its use. In this paper, an entropy-constrained residual vector quantization method is proposed for lossless compression of images. The method consists of first quantizing the input image using a high order entropy-constrained residual vector quantizer and then coding the residual image using a first order entropy coder. The distortion measure used in the entropy-constrained optimization is essentially the first order entropy of the residual image. Experimental results show very competitive performance.

  17. Geometric entropy and edge modes of the electromagnetic field

    NASA Astrophysics Data System (ADS)

    Donnelly, William; Wall, Aron C.

    2016-11-01

    We calculate the vacuum entanglement entropy of Maxwell theory in a class of curved spacetimes by Kaluza-Klein reduction of the theory onto a two-dimensional base manifold. Using two-dimensional duality, we express the geometric entropy of the electromagnetic field as the entropy of a tower of scalar fields, constant electric and magnetic fluxes, and a contact term, whose leading-order divergence was discovered by Kabat. The complete contact term takes the form of one negative scalar degree of freedom confined to the entangling surface. We show that the geometric entropy agrees with a statistical definition of entanglement entropy that includes edge modes: classical solutions determined by their boundary values on the entangling surface. This resolves a long-standing puzzle about the statistical interpretation of the contact term in the entanglement entropy. We discuss the implications of this negative term for black hole thermodynamics and the renormalization of Newton's constant.

  18. Relative entropy equals bulk relative entropy

    SciTech Connect

    Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan; Suh, S. Josephine

    2016-06-01

    We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

  19. On variational definition of quantum entropy

    SciTech Connect

    Belavkin, Roman V.

    2015-01-13

    Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information.

  20. Entropy and econophysics

    NASA Astrophysics Data System (ADS)

    Rosser, J. Barkley

    2016-12-01

    Entropy is a central concept of statistical mechanics, which is the main branch of physics that underlies econophysics, the application of physics concepts to understand economic phenomena. It enters into econophysics both in an ontological way through the Second Law of Thermodynamics as this drives the world economy from its ecological foundations as solar energy passes through food chains in dissipative process of entropy rising and production fundamentally involving the replacement of lower entropy energy states with higher entropy ones. In contrast the mathematics of entropy as appearing in information theory becomes the basis for modeling financial market dynamics as well as income and wealth distribution dynamics. It also provides the basis for an alternative view of stochastic price equilibria in economics, as well providing a crucial link between econophysics and sociophysics, keeping in mind the essential unity of the various concepts of entropy.

  1. Single water entropy: hydrophobic crossover and application to drug binding.

    PubMed

    Sasikala, Wilbee D; Mukherjee, Arnab

    2014-09-11

    Entropy of water plays an important role in both chemical and biological processes e.g. hydrophobic effect, molecular recognition etc. Here we use a new approach to calculate translational and rotational entropy of the individual water molecules around different hydrophobic and charged solutes. We show that for small hydrophobic solutes, the translational and rotational entropies of each water molecule increase as a function of its distance from the solute reaching finally to a constant bulk value. As the size of the solute increases (0.746 nm), the behavior of the translational entropy is opposite; water molecules closest to the solute have higher entropy that reduces with distance from the solute. This indicates that there is a crossover in translational entropy of water molecules around hydrophobic solutes from negative to positive values as the size of the solute is increased. Rotational entropy of water molecules around hydrophobic solutes for all sizes increases with distance from the solute, indicating the absence of crossover in rotational entropy. This makes the crossover in total entropy (translation + rotation) of water molecule happen at much larger size (>1.5 nm) for hydrophobic solutes. Translational entropy of single water molecule scales logarithmically (Str(QH) = C + kB ln V), with the volume V obtained from the ellipsoid of inertia. We further discuss the origin of higher entropy of water around water and show the possibility of recovering the entropy loss of some hypothetical solutes. The results obtained are helpful to understand water entropy behavior around various hydrophobic and charged environments within biomolecules. Finally, we show how our approach can be used to calculate the entropy of the individual water molecules in a protein cavity that may be replaced during ligand binding.

  2. The Holographic Entropy Cone

    SciTech Connect

    Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael

    2015-09-21

    We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

  3. The Holographic Entropy Cone

    DOE PAGES

    Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; ...

    2015-09-21

    We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phasemore » space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.« less

  4. Theory of entropy production in quantum many-body systems

    NASA Astrophysics Data System (ADS)

    Solano-Carrillo, E.; Millis, A. J.

    2016-06-01

    We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second, and third laws of thermodynamics. For weakly coupled subsystems of an isolated system, an expression for the long-time limit of the expectation value of the rate of change of the thermodynamically measurable part of the entropy operator is derived and interpreted in terms of entropy production and entropy transport terms. The interpretation is justified by comparison to the known expression for the entropy production in an aged classical Markovian system with Gaussian fluctuations and by a calculation of the current-induced entropy production in a conductor with electron-phonon scattering.

  5. Charged topological entanglement entropy

    NASA Astrophysics Data System (ADS)

    Matsuura, Shunji; Wen, Xueda; Hung, Ling-Yan; Ryu, Shinsei

    2016-05-01

    A charged entanglement entropy is a new measure which probes quantum entanglement between different charge sectors. We study symmetry-protected topological (SPT) phases in (2+1)-dimensional space-time by using this charged entanglement entropy. SPT phases are short-range entangled states without topological order and hence cannot be detected by the topological entanglement entropy. We demonstrate that the universal part of the charged entanglement entropy is nonzero for nontrivial SPT phases and therefore it is a useful measure to detect short-range entangled topological phases. We also discuss that the classification of SPT phases based on the charged topological entanglement entropy is related to that of the braiding statistics of quasiparticles.

  6. Repositioning Recitation Input in College English Teaching

    ERIC Educational Resources Information Center

    Xu, Qing

    2009-01-01

    This paper tries to discuss how recitation input helps overcome the negative influences on the basis of second language acquisition theory and confirms the important role that recitation input plays in improving college students' oral and written English.

  7. Effects of correlated variability on information entropies in nonextensive systems

    NASA Astrophysics Data System (ADS)

    Hasegawa, Hideo

    2008-08-01

    We have calculated the Tsallis entropy and Fisher information matrix (entropy) of spatially correlated nonextensive systems, by using an analytic non-Gaussian distribution obtained by the maximum entropy method. The effects of the correlated variability on the Fisher information matrix are shown to be different from those on the Tsallis entropy. The Fisher information is increased (decreased) by a positive (negative) correlation, whereas the Tsallis entropy is decreased with increasing absolute magnitude of the correlation, independently of its sign. This fact arises from the difference in their characteristics. It implies from the Cramér-Rao inequality that the accuracy of an unbiased estimate of fluctuation is improved by a negative correlation. A critical comparison is made between the present study and previous ones employing the Gaussian approximation for the correlated variability due to multiplicative noise.

  8. Continuity of the entropy of macroscopic quantum systems.

    PubMed

    Swendsen, Robert H

    2015-11-01

    The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large but finite quantum mechanical systems. A special feature of this analysis is that the thermodynamic energy of a quantum system is shown to be a continuous variable, rather than being associated with discrete energy eigenvalues. Calculations of the entropy as a function of energy can be carried out with a Legendre transform of thermodynamic potentials obtained from a canonical ensemble. The resultant expressions for the entropy are able to describe equilibrium between quantum systems having incommensurate energy-level spacings. This definition of entropy preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics. It demonstrates the consistency of the concept of negative temperature with the principles of thermodynamics.

  9. Entropy and biological systems: Experimentally-investigated entropy-driven stacking of plant photosynthetic membranes

    NASA Astrophysics Data System (ADS)

    Jia, Husen; Liggins, John R.; Chow, Wah Soon

    2014-02-01

    According to the Second Law of Thermodynamics, an overall increase of entropy contributes to the driving force for any physicochemical process, but entropy has seldom been investigated in biological systems. Here, for the first time, we apply Isothermal Titration Calorimetry (ITC) to investigate the Mg2+-induced spontaneous stacking of photosynthetic membranes isolated from spinach leaves. After subtracting a large endothermic interaction of MgCl2 with membranes, unrelated to stacking, we demonstrate that the enthalpy change (heat change at constant pressure) is zero or marginally positive or negative. This first direct experimental evidence strongly suggests that an entropy increase significantly drives membrane stacking in this ordered biological structure. Possible mechanisms for the entropy increase include: (i) the attraction between discrete oppositely-charged areas, releasing counterions; (ii) the release of loosely-bound water molecules from the inter-membrane gap; (iii) the increased orientational freedom of previously-aligned water dipoles; and (iv) the lateral rearrangement of membrane components.

  10. Characterizing Component Hiding Using Ancestral Entropy

    DTIC Science & Technology

    2009-03-26

    placed. The maximum entropy value for experiment is 1 because the right uppermost circuit in Figure A.15(a) is preserved. Two ancestors are in 776 of...Input 11 Input Output Level .137 .273 .136 Node .005 .595 .002 Circuit Level . 013 .459 0.000 4.9. Table 4.2 contains the p values from the 2-Sample t...03.03shortstories/. 12. McDonald, Jeffrey T. Enhanced Security for Mobile Agent Systems. Ph.D. thesis, Florida State University, 2006. 13. Mish

  11. The Mystique of Entropy.

    ERIC Educational Resources Information Center

    Kyle, Benjamin G.

    1988-01-01

    Illustrates qualitative and metaphoric applications of entropy in the areas of cosmology, the birth and death of the universe and time; life and evolution; literature and art; and social science. (RT)

  12. Absolute Equilibrium Entropy

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    1997-01-01

    The entropy associated with absolute equilibrium ensemble theories of ideal, homogeneous, fluid and magneto-fluid turbulence is discussed and the three-dimensional fluid case is examined in detail. A sigma-function is defined, whose minimum value with respect to global parameters is the entropy. A comparison is made between the use of global functions sigma and phase functions H (associated with the development of various H-theorems of ideal turbulence). It is shown that the two approaches are complimentary though conceptually different: H-theorems show that an isolated system tends to equilibrium while sigma-functions allow the demonstration that entropy never decreases when two previously isolated systems are combined. This provides a more complete picture of entropy in the statistical mechanics of ideal fluids.

  13. Intermediate inputs and economic productivity.

    PubMed

    Baptist, Simon; Hepburn, Cameron

    2013-03-13

    Many models of economic growth exclude materials, energy and other intermediate inputs from the production function. Growing environmental pressures and resource prices suggest that this may be increasingly inappropriate. This paper explores the relationship between intermediate input intensity, productivity and national accounts using a panel dataset of manufacturing subsectors in the USA over 47 years. The first contribution is to identify sectoral production functions that incorporate intermediate inputs, while allowing for heterogeneity in both technology and productivity. The second contribution is that the paper finds a negative correlation between intermediate input intensity and total factor productivity (TFP)--sectors that are less intensive in their use of intermediate inputs have higher productivity. This finding is replicated at the firm level. We propose tentative hypotheses to explain this association, but testing and further disaggregation of intermediate inputs is left for further work. Further work could also explore more directly the relationship between material inputs and economic growth--given the high proportion of materials in intermediate inputs, the results in this paper are suggestive of further work on material efficiency. Depending upon the nature of the mechanism linking a reduction in intermediate input intensity to an increase in TFP, the implications could be significant. A third contribution is to suggest that an empirical bias in productivity, as measured in national accounts, may arise due to the exclusion of intermediate inputs. Current conventions of measuring productivity in national accounts may overstate the productivity of resource-intensive sectors relative to other sectors.

  14. Physics of negative absolute temperatures

    NASA Astrophysics Data System (ADS)

    Abraham, Eitan; Penrose, Oliver

    2017-01-01

    Negative absolute temperatures were introduced into experimental physics by Purcell and Pound, who successfully applied this concept to nuclear spins; nevertheless, the concept has proved controversial: a recent article aroused considerable interest by its claim, based on a classical entropy formula (the "volume entropy") due to Gibbs, that negative temperatures violated basic principles of statistical thermodynamics. Here we give a thermodynamic analysis that confirms the negative-temperature interpretation of the Purcell-Pound experiments. We also examine the principal arguments that have been advanced against the negative temperature concept; we find that these arguments are not logically compelling, and moreover that the underlying "volume" entropy formula leads to predictions inconsistent with existing experimental results on nuclear spins. We conclude that, despite the counterarguments, negative absolute temperatures make good theoretical sense and did occur in the experiments designed to produce them.

  15. Excitation entanglement entropy in two dimensional conformal field theories

    NASA Astrophysics Data System (ADS)

    Sheikh-Jabbari, M. M.; Yavartanoo, H.

    2016-12-01

    We analyze how excitations affect the entanglement entropy for an arbitrary entangling interval in a 2d conformal field theory (CFT) using the holographic entanglement entropy techniques as well as direct CFT computations. We introduce the excitation entanglement entropy ΔhS , the difference between the entanglement entropy generic excitations and their arbitrary conformal descendants denoted through h . The excitation entanglement entropy, unlike the entanglement entropy, is a finite quantity (independent of the cutoff), and hence a good physical observable. We show that the excitation entanglement entropy for any given interval is uniquely specified by a local second order differential equation sourced by the one point function of the energy momentum tensor computed in the excited background state, and two boundary and smoothness conditions. We analyze low and high temperature behavior of the excitation entanglement entropy and show that ΔhS grows as a function of temperature. We prove an "integrated positivity" for the excitation entanglement entropy, that although ΔhS can be positive or negative, its average value is always positive. We also discuss the mutual and multipartite information and (strong) subadditivity inequality in the presence of generic excitations and their conformal descendants.

  16. Comparison of canonical and microcanonical definitions of entropy

    NASA Astrophysics Data System (ADS)

    Matty, Michael; Lancaster, Lachlan; Griffin, William; Swendsen, Robert H.

    2017-02-01

    For more than 100 years, one of the central concepts in statistical mechanics has been the microcanonical ensemble, which provides a way of calculating the thermodynamic entropy for a specified energy. A controversy has recently emerged between two distinct definitions of the entropy based on the microcanonical ensemble: (1) The Boltzmann entropy, defined by the density of states at a specified energy, and (2) The Gibbs entropy, defined by the sum or integral of the density of states below a specified energy. A critical difference between the consequences of these definitions pertains to the concept of negative temperatures, which by the Gibbs definition cannot exist. In this paper, we call into question the fundamental assumption that the microcanonical ensemble should be used to define the entropy. We base our analysis on a recently proposed canonical definition of the entropy as a function of energy. We investigate the predictions of the Boltzmann, Gibbs, and canonical definitions for a variety of classical and quantum models. Our results support the validity of the concept of negative temperature, but not for all models with a decreasing density of states. We find that only the canonical entropy consistently predicts the correct thermodynamic properties, while microcanonical definitions of entropy, including those of Boltzmann and Gibbs, are correct only for a limited set of models. For models which exhibit a first-order phase transition, we show that the use of the thermodynamic limit, as usually interpreted, can conceal the essential physics.

  17. Connectivity in the human brain dissociates entropy and complexity of auditory inputs☆

    PubMed Central

    Nastase, Samuel A.; Iacovella, Vittorio; Davis, Ben; Hasson, Uri

    2015-01-01

    Complex systems are described according to two central dimensions: (a) the randomness of their output, quantified via entropy; and (b) their complexity, which reflects the organization of a system's generators. Whereas some approaches hold that complexity can be reduced to uncertainty or entropy, an axiom of complexity science is that signals with very high or very low entropy are generated by relatively non-complex systems, while complex systems typically generate outputs with entropy peaking between these two extremes. In understanding their environment, individuals would benefit from coding for both input entropy and complexity; entropy indexes uncertainty and can inform probabilistic coding strategies, whereas complexity reflects a concise and abstract representation of the underlying environmental configuration, which can serve independent purposes, e.g., as a template for generalization and rapid comparisons between environments. Using functional neuroimaging, we demonstrate that, in response to passively processed auditory inputs, functional integration patterns in the human brain track both the entropy and complexity of the auditory signal. Connectivity between several brain regions scaled monotonically with input entropy, suggesting sensitivity to uncertainty, whereas connectivity between other regions tracked entropy in a convex manner consistent with sensitivity to input complexity. These findings suggest that the human brain simultaneously tracks the uncertainty of sensory data and effectively models their environmental generators. PMID:25536493

  18. Entropy of stochastic flows

    SciTech Connect

    Dorogovtsev, Andrei A

    2010-06-29

    For sets in a Hilbert space the concept of quadratic entropy is introduced. It is shown that this entropy is finite for the range of a stochastic flow of Brownian particles on R. This implies, in particular, the fact that the total time of the free travel in the Arratia flow of all particles that started from a bounded interval is finite. Bibliography: 10 titles.

  19. Entropy of quasiblack holes

    SciTech Connect

    Lemos, Jose P. S.; Zaslavskii, Oleg B.

    2010-03-15

    We trace the origin of the black hole entropy S, replacing a black hole by a quasiblack hole. Let the boundary of a static body approach its own gravitational radius, in such a way that a quasihorizon forms. We show that if the body is thermal with the temperature taking the Hawking value at the quasihorizon limit, it follows, in the nonextremal case, from the first law of thermodynamics that the entropy approaches the Bekenstein-Hawking value S=A/4. In this setup, the key role is played by the surface stresses on the quasihorizon and one finds that the entropy comes from the quasihorizon surface. Any distribution of matter inside the surface leads to the same universal value for the entropy in the quasihorizon limit. This can be of some help in the understanding of black hole entropy. Other similarities between black holes and quasiblack holes such as the mass formulas for both objects had been found previously. We also discuss the entropy for extremal quasiblack holes, a more subtle issue.

  20. Entropy and environmental mystery.

    PubMed

    Stamps, Arthur E

    2007-06-01

    Two studies are reported regarding the effects of entropy, lighting, and occlusion on impressions of mystery in physical environments. The theoretical context of this study was the "informational theory" of environmental preference, which, among other claims, holds that mystery can be measured by the extent to which people perceive a promise of more information if they move deeper into an environment. Entropy, in the context of this article, is visual diversity as measured using information theory. Mystery was measured by a semantic differential scale. The definition of mystery was left up to each individual participant. Entropy of occluded objects was used to obtain an objective, experimentally manipulatable and operational definition of "promise of more information." Exp. 1 had 12 stimuli and 15 participants. Exp. 2 had 12 stimuli and 16 participants. Entropy of occluded objects ranged from 0 to 6 bits. Entropy of occluded objects was used to measure the promise that there would be more information if one moved deeper into an environment. Overall, amount of light had the strongest effect on responses of mystery (r = -.63, darker was more mysterious), followed by occlusion (r = .26, occluding objects made a scene seem more mysterious), and by the promise of more information if one moved about in the scene (r = .13), the more entropy in occluded objects, the greater the impression of mystery). The theoretical contribution of this work is that a relationship between subjective impressions of mystery and an objective measure of "promise of more information" was found.

  1. Renormalized entanglement entropy

    NASA Astrophysics Data System (ADS)

    Taylor, Marika; Woodhead, William

    2016-08-01

    We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement en-tropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renor-malization group flows. The renormalized entanglement entropy for disk regions in AdS 4 spacetimes agrees precisely with the holographically renormalized action for AdS 4 with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deforma-tions by operators of dimension 3 /2 < Δ < 5 /2 for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our renormalization method for the entangle-ment entropy is inherited directly from that of the partition function. We show explicitly how the entanglement entropy counterterms can be derived from the standard holographic renormalization counterterms for asymptotically locally anti-de Sitter spacetimes.

  2. Entropy, matter, and cosmology

    PubMed Central

    Prigogine, I.; Géhéniau, J.

    1986-01-01

    The role of irreversible processes corresponding to creation of matter in general relativity is investigated. The use of Landau-Lifshitz pseudotensors together with conformal (Minkowski) coordinates suggests that this creation took place in the early universe at the stage of the variation of the conformal factor. The entropy production in this creation process is calculated. It is shown that these dissipative processes lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Gravitational entropy takes a simple meaning as associated to the entropy that is necessary to produce matter. This leads to an extension of the third law of thermodynamics, as now the zero point of entropy becomes the space-time structure out of which matter is generated. The theory can be put into a convenient form using a supplementary “C” field in Einstein's field equations. The role of the C field is to express the coupling between gravitation and matter leading to irreversible entropy production. PMID:16593747

  3. Information Entropy of Fullerenes.

    PubMed

    Sabirov, Denis Sh; Ōsawa, Eiji

    2015-08-24

    The reasons for the formation of the highly symmetric C60 molecule under nonequilibrium conditions are widely discussed as it dominates over numerous similar fullerene structures. In such conditions, evolution of structure rather than energy defines the processes. We have first studied the diversity of fullerenes in terms of information entropy. Sorting 2079 structures from An Atlas of Fullerenes [ Fowler , P. W. ; Manolopoulos , D. E. An Atlas of Fullerenes ; Oxford : Clarendon , 1995 . ], we have found that the information entropies of only 14 fullerenes (<1% of the studied structures) lie between the values of C60 and C70, the two most abundant fullerenes. Interestingly, buckminsterfullerene is the only fullerene with zero information entropy, i.e., an exclusive compound among the other members of the fullerene family. Such an efficient sorting demonstrates possible relevance of information entropy to chemical processes. For this reason, we have introduced an algorithm for calculating changes in information entropy at chemical transformations. The preliminary calculations of changes in information entropy at the selected fullerene reactions show good agreement with thermochemical data.

  4. Differential entropy and time

    NASA Astrophysics Data System (ADS)

    Garbaczewski, Piotr

    2005-12-01

    We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage of conditional Kullback-Leibler and Gibbs (Shannon) entropies is explained in case of non-equilibrium Smoluchowski processes. A very different temporal behavior of Gibbs and Kullback entropies is confronted. A specific conceptual niche is addressed, where quantum von Neumann, classical Kullback-Leibler and Gibbs entropies can be consistently introduced as information measures for the same physical system. If the dynamics of probability densities is driven by the Schrödinger picture wave-packet evolution, Gibbs-type and related Fisher information functionals appear to quantify nontrivial power transfer processes in the mean. This observation is found to extend to classical dissipative processes and supports the view that the Shannon entropy dynamics provides an insight into physically relevant non-equilibrium phenomena, which are inaccessible in terms of the Kullback-Leibler entropy and typically ignored in the literature.

  5. The continuity of the output entropy of positive maps

    SciTech Connect

    Shirokov, Maxim E

    2011-10-31

    Global and local continuity conditions for the output von Neumann entropy for positive maps between Banach spaces of trace-class operators in separable Hilbert spaces are obtained. Special attention is paid to completely positive maps: infinite dimensional quantum channels and operations. It is shown that as a result of some specific properties of the von Neumann entropy (as a function on the set of density operators) several results on the output entropy of positive maps can be obtained, which cannot be derived from the general properties of entropy type functions. In particular, it is proved that global continuity of the output entropy of a positive map follows from its finiteness. A characterization of positive linear maps preserving continuity of the entropy (in the following sense: continuity of the entropy on an arbitrary subset of input operators implies continuity of the output entropy on this subset) is obtained. A connection between the local continuity properties of two completely positive complementary maps is considered. Bibliography: 21 titles.

  6. Upper bound for the average entropy production based on stochastic entropy extrema

    NASA Astrophysics Data System (ADS)

    Limkumnerd, Surachate

    2017-03-01

    The second law of thermodynamics, which asserts the non-negativity of the average total entropy production of a combined system and its environment, is a direct consequence of applying Jensen's inequality to a fluctuation relation. It is also possible, through this inequality, to determine an upper bound of the average total entropy production based on the entropies along the most extreme stochastic trajectories. In this work, we construct an upper bound inequality of the average of a convex function over a domain whose average is known. When applied to the various fluctuation relations, the upper bounds of the average total entropy production are established. Finally, by employing the result of Neri, Roldán, and Jülicher [Phys. Rev. X 7, 011019 (2017)], 10.1103/PhysRevX.7.011019, we are able to show that the average total entropy production is bounded only by the total entropy production supremum, and vice versa, for a general nonequilibrium stationary system.

  7. On Entropy Trail

    NASA Astrophysics Data System (ADS)

    Farokhi, Saeed; Taghavi, Ray; Keshmiri, Shawn

    2015-11-01

    Stealth technology is developed for military aircraft to minimize their signatures. The primary attention was focused on radar signature, followed by the thermal and noise signatures of the vehicle. For radar evasion, advanced configuration designs, extensive use of carbon composites and radar-absorbing material, are developed. On thermal signature, mainly in the infra-red (IR) bandwidth, the solution was found in blended rectangular nozzles of high aspect ratio that are shielded from ground detectors. For noise, quiet and calm jets are integrated into vehicles with low-turbulence configuration design. However, these technologies are totally incapable of detecting new generation of revolutionary aircraft. These shall use all electric, distributed, propulsion system that are thermally transparent. In addition, composite skin and non-emitting sensors onboard the aircraft will lead to low signature. However, based on the second-law of thermodynamics, there is no air vehicle that can escape from leaving an entropy trail. Entropy is thus the only inevitable signature of any system, that once measured, can detect the source. By characterizing the entropy field based on its statistical properties, the source may be recognized, akin to face recognition technology. Direct measurement of entropy is cumbersome, however as a derived property, it can be easily measured. The measurement accuracy depends on the probe design and the sensors onboard. One novel air data sensor suite is introduced with promising potential to capture the entropy trail.

  8. Entropy, color, and color rendering.

    PubMed

    Price, Luke L A

    2012-12-01

    The Shannon entropy [Bell Syst. Tech J.27, 379 (1948)] of spectral distributions is applied to the problem of color rendering. With this novel approach, calculations for visual white entropy, spectral entropy, and color rendering are proposed, indices that are unreliant on the subjectivity inherent in reference spectra and color samples. The indices are tested against real lamp spectra, showing a simple and robust system for color rendering assessment. The discussion considers potential roles for white entropy in several areas of color theory and psychophysics and nonextensive entropy generalizations of the entropy indices in mathematical color spaces.

  9. Sharp continuity bounds for entropy and conditional entropy

    NASA Astrophysics Data System (ADS)

    Chen, ZhiHua; Ma, ZhiHao; Nikoufar, Ismail; Fei, Shao-Ming

    2017-02-01

    The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is derived. This inequality is shown to be tight in the sense that equality can be attained for every prescribed value of the trace norm distance. It includes the sharp Fannes inequality for von Neumann entropy as a special case.

  10. EEG entropy measures in anesthesia

    PubMed Central

    Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J.; Sleigh, Jamie W.; Hagihira, Satoshi; Li, Xiaoli

    2015-01-01

    Highlights: ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Methods: Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation

  11. Enthalpy-entropy compensation: the role of solvation.

    PubMed

    Dragan, Anatoliy I; Read, Christopher M; Crane-Robinson, Colyn

    2017-05-01

    Structural modifications to interacting systems frequently lead to changes in both the enthalpy (heat) and entropy of the process that compensate each other, so that the Gibbs free energy is little changed: a major barrier to the development of lead compounds in drug discovery. The conventional explanation for such enthalpy-entropy compensation (EEC) is that tighter contacts lead to a more negative enthalpy but increased molecular constraints, i.e., a compensating conformational entropy reduction. Changes in solvation can also contribute to EEC but this contribution is infrequently discussed. We review long-established and recent cases of EEC and conclude that the large fluctuations in enthalpy and entropy observed are too great to be a result of only conformational changes and must result, to a considerable degree, from variations in the amounts of water immobilized or released on forming complexes. Two systems exhibiting EEC show a correlation between calorimetric entropies and local mobilities, interpreted to mean conformational control of the binding entropy/free energy. However, a substantial contribution from solvation gives the same effect, as a consequence of a structural link between the amount of bound water and the protein flexibility. Only by assuming substantial changes in solvation-an intrinsically compensatory process-can a more complete understanding of EEC be obtained. Faced with such large, and compensating, changes in the enthalpies and entropies of binding, the best approach to engineering elevated affinities must be through the addition of ionic links, as they generate increased entropy without affecting the enthalpy.

  12. Information entropy in cosmology.

    PubMed

    Hosoya, Akio; Buchert, Thomas; Morita, Masaaki

    2004-04-09

    The effective evolution of an inhomogeneous cosmological model may be described in terms of spatially averaged variables. We point out that in this context, quite naturally, a measure arises which is identical to a fluid model of the Kullback-Leibler relative information entropy, expressing the distinguishability of the local inhomogeneous mass density field from its spatial average on arbitrary compact domains. We discuss the time evolution of "effective information" and explore some implications. We conjecture that the information content of the Universe-measured by relative information entropy of a cosmological model containing dust matter-is increasing.

  13. Angular momentum independence of the entropy sum and entropy product for AdS rotating black holes in all dimensions

    NASA Astrophysics Data System (ADS)

    Liu, Hang; Meng, Xin-he

    2016-08-01

    In this paper, we investigate the angular momentum independence of the entropy sum and product for AdS rotating black holes based on the first law of thermodynamics and a mathematical lemma related to Vandermonde determinant. The advantage of this method is that the explicit forms of the spacetime metric, black hole mass and charge are not needed but the Hawking temperature and entropy formula on the horizons are necessary for static black holes, while our calculations require the expressions of metric and angular velocity formula. We find that the entropy sum is always independent of angular momentum for all dimensions and the angular momentum-independence of entropy product only holds for the dimensions d > 4 with at least one rotation parameter ai = 0, while the mass-free of entropy sum and entropy product for rotating black holes only stand for higher dimensions (d > 4) and for all dimensions, respectively. On the other hand, we find that the introduction of a negative cosmological constant does not affect the angular momentum-free of entropy sum and product but the criterion for angular momentum-independence of entropy product will be affected.

  14. Entropy squeezing for qubit – field system under decoherence effect

    SciTech Connect

    Abdel-Khalek, S; Berrada, K; A-S F Obada; Wahiddin, M R

    2014-03-28

    We study in detail the dynamics of field entropy squeezing (FES) for a qubit – field system whose dynamics is described by the phase-damped model. The results of calculations show that the initial state and decoherence play a crucial role in the evolution of FES. During the temporal evolution of the system under decoherence effect, an interesting monotonic relation between FES, Wehrl entropy (WE) and negativity is observed. (laser applications and other topics in quantum electronics)

  15. Optimized Kernel Entropy Components.

    PubMed

    Izquierdo-Verdiguier, Emma; Laparra, Valero; Jenssen, Robert; Gomez-Chova, Luis; Camps-Valls, Gustau

    2016-02-25

    This brief addresses two main issues of the standard kernel entropy component analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of variance, as in the kernel principal components analysis. In this brief, we propose an extension of the KECA method, named optimized KECA (OKECA), that directly extracts the optimal features retaining most of the data entropy by means of compacting the information in very few features (often in just one or two). The proposed method produces features which have higher expressive power. In particular, it is based on the independent component analysis framework, and introduces an extra rotation to the eigen decomposition, which is optimized via gradient-ascent search. This maximum entropy preservation suggests that OKECA features are more efficient than KECA features for density estimation. In addition, a critical issue in both the methods is the selection of the kernel parameter, since it critically affects the resulting performance. Here, we analyze the most common kernel length-scale selection criteria. The results of both the methods are illustrated in different synthetic and real problems. Results show that OKECA returns projections with more expressive power than KECA, the most successful rule for estimating the kernel parameter is based on maximum likelihood, and OKECA is more robust to the selection of the length-scale parameter in kernel density estimation.

  16. Rescaling Temperature and Entropy

    ERIC Educational Resources Information Center

    Olmsted, John, III

    2010-01-01

    Temperature and entropy traditionally are expressed in units of kelvin and joule/kelvin. These units obscure some important aspects of the natures of these thermodynamic quantities. Defining a rescaled temperature using the Boltzmann constant, T' = k[subscript B]T, expresses temperature in energy units, thereby emphasizing the close relationship…

  17. Entropy of the Universe

    NASA Astrophysics Data System (ADS)

    Sato, Humitaka

    2010-06-01

    Charles Darwin's calculation of a life of Earth had ignited Kelvin's insight on a life of Sun, which had eventually inherited to the physical study of stellar structure and energy source. Nuclear energy had secured a longevity of the universe and the goal of the cosmic evolution has been secured by the entropy of black holes.

  18. Entropy and cosmology.

    NASA Astrophysics Data System (ADS)

    Zucker, M. H.

    This paper is a critical analysis and reassessment of entropic functioning as it applies to the question of whether the ultimate fate of the universe will be determined in the future to be "open" (expanding forever to expire in a big chill), "closed" (collapsing to a big crunch), or "flat" (balanced forever between the two). The second law of thermodynamics declares that entropy can only increase and that this principle extends, inevitably, to the universe as a whole. This paper takes the position that this extension is an unwarranted projection based neither on experience nonfact - an extrapolation that ignores the powerful effect of a gravitational force acting within a closed system. Since it was originally presented by Clausius, the thermodynamic concept of entropy has been redefined in terms of "order" and "disorder" - order being equated with a low degree of entropy and disorder with a high degree. This revised terminology more subjective than precise, has generated considerable confusion in cosmology in several critical instances. For example - the chaotic fireball of the big bang, interpreted by Stephen Hawking as a state of disorder (high entropy), is infinitely hot and, thermally, represents zero entropy (order). Hawking, apparently focusing on the disorderly "chaotic" aspect, equated it with a high degree of entropy - overlooking the fact that the universe is a thermodynamic system and that the key factor in evaluating the big-bang phenomenon is the infinitely high temperature at the early universe, which can only be equated with zero entropy. This analysis resolves this confusion and reestablishes entropy as a cosmological function integrally linked to temperature. The paper goes on to show that, while all subsystems contained within the universe require external sources of energization to have their temperatures raised, this requirement does not apply to the universe as a whole. The universe is the only system that, by itself can raise its own

  19. Entropy Production in Convective Hydrothermal Systems

    NASA Astrophysics Data System (ADS)

    Boersing, Nele; Wellmann, Florian; Niederau, Jan

    2016-04-01

    Rayleigh number and moderate aspect ratio, entropy production even enables to predict a preferred convection mode for a model with homogeneous parameter distribution. As a general rule, the thermodynamic measure of entropy production can be used to analyze uncertainties accompanied by modelling convective hydrothermal systems. Without considering any probability distributions of input data, this synthetic study shows that a higher entropy production implies a lower ability to uniquely predict the convection pattern. This in turn means that the uncertainty in estimating subsurface temperatures is higher.

  20. The equivalence of minimum entropy production and maximum thermal efficiency in endoreversible heat engines.

    PubMed

    Haseli, Y

    2016-05-01

    The objective of this study is to investigate the thermal efficiency and power production of typical models of endoreversible heat engines at the regime of minimum entropy generation rate. The study considers the Curzon-Ahlborn engine, the Novikov's engine, and the Carnot vapor cycle. The operational regimes at maximum thermal efficiency, maximum power output and minimum entropy production rate are compared for each of these engines. The results reveal that in an endoreversible heat engine, a reduction in entropy production corresponds to an increase in thermal efficiency. The three criteria of minimum entropy production, the maximum thermal efficiency, and the maximum power may become equivalent at the condition of fixed heat input.

  1. Diffusive mixing and Tsallis entropy

    DOE PAGES

    O'Malley, Daniel; Vesselinov, Velimir V.; Cushman, John H.

    2015-04-29

    Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis q-entropy, which is non-additive, was developed as an alternative to the classical entropy for systems which are non-ergodic. A generalization of Brownian motion is provided that maximizes the Tsallis entropy rather than the Boltzmann-Gibbs entropy. This process is driven by a Brownian measure with a random diffusion coefficient. In addition, the distribution of this coefficient is derived as a function of q for 1 < q < 3. Applications to transport in porous media are considered.

  2. The different paths to entropy

    NASA Astrophysics Data System (ADS)

    Benguigui, L.

    2013-03-01

    In order to understand how the complex concept of entropy emerged, we propose a trip into the past, reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since Gibbs's work is not very well known we present a detailed analysis, recalling the three definitions of entropy that Gibbs gives. The introduction of entropy in quantum mechanics gives in a compact form all the classical definitions of entropy. Perhaps one of the most important aspects of entropy is to see it as a thermodynamic potential like the others proposed by Callen. The calculation of fluctuations in thermodynamic quantities is thus naturally related to entropy. We close with some remarks on entropy and irreversibility.

  3. Local Entropy, Metric Entropy and Topological Entropy for Countable Discrete Amenable Group Actions

    NASA Astrophysics Data System (ADS)

    Ren, Xiankun; Sun, Wenxiang

    2016-06-01

    Let X be a compact metric space and G a countable infinite discrete amenable group acting on X. Like in the ℤ-action cases we define the notion of local entropy and by it we bound the difference between metric entropy and that of a partition, and bound the difference between topological entropy and that of a separated set, which generalize Theorems 1(1) and 1(2) in [Newhouse, 1989] from ℤ-actions to amenable group actions. We further prove that the entropy function hμ(G) is upper semi-continuous on ℳ(X,G) for an asymptotic entropy expansive amenable group action.

  4. Entropy-stabilized oxides

    PubMed Central

    Rost, Christina M.; Sachet, Edward; Borman, Trent; Moballegh, Ali; Dickey, Elizabeth C.; Hou, Dong; Jones, Jacob L.; Curtarolo, Stefano; Maria, Jon-Paul

    2015-01-01

    Configurational disorder can be compositionally engineered into mixed oxide by populating a single sublattice with many distinct cations. The formulations promote novel and entropy-stabilized forms of crystalline matter where metal cations are incorporated in new ways. Here, through rigorous experiments, a simple thermodynamic model, and a five-component oxide formulation, we demonstrate beyond reasonable doubt that entropy predominates the thermodynamic landscape, and drives a reversible solid-state transformation between a multiphase and single-phase state. In the latter, cation distributions are proven to be random and homogeneous. The findings validate the hypothesis that deliberate configurational disorder provides an orthogonal strategy to imagine and discover new phases of crystalline matter and untapped opportunities for property engineering. PMID:26415623

  5. Avoiding the entropy trap

    SciTech Connect

    Weinberg, A.M.

    1982-10-01

    Utopians who use entropy to warn of a vast deterioration of energy and mineral resources seek a self-fulfilling prophesy when they work to deny society access to new energy sources, particularly nuclear power. While theoretically correct, entropy is not the relevant factor for the rest of this century. The more extreme entropists call for a return to an eotechnic society based on decentralized, renewable energy technologies, which rests on the assumptions of a loss in Gibbs Free Energy, a mineral depletion that will lead to OPEC-like manipulation, and a current technology that is destroying the environment. The author challenges these assumptions and calls for an exorcism of public fears over reactor accidents. He foresees a resurgence in public confidence in nuclear power by 1990 that will resolve Western dependence on foreign oil. (DCK)

  6. Entropy and information optics

    NASA Astrophysics Data System (ADS)

    Yu, Francis T. S.

    2000-03-01

    In this paper we shall begin our discussion with the relationship between optics and humans, in which we see that light has indeed provided us with a very valuable source of information. A general optical communication concept is discussed, in which we see that a picture is indeed worth more than a thousand words. Based on Shannon's information theory, one can show that entropy and information can be simply traded. One of the most intriguing laws of thermodynamics must be the second law, in which we have found that there exists a profound relationship between the physical entropy and information. Without this relationship, information theory would be totally useless in physical science. By applying this relationship, Maxwell and diffraction-limited demons are discussed. And finally, samples of information optics are provided.

  7. Relative Entropy Credibility Theory

    NASA Astrophysics Data System (ADS)

    Fernández-Durán, Juan José; Gregorio-Domínguez, María Mercedes

    2004-11-01

    Consider a portfolio of personal motor insurance policies in which, for each policyholder in the portfolio, we want to assign a credibility factor at the end of each policy period that reflects the claim experience of the policyholder compared with the claim experience of the entire portfolio. In this paper we present the calculation of credibility factors based on the concept of relative entropy between the claim size distribution of the entire portfolio and the claim size distribution of the policyholder.

  8. Quantum and Ecosystem Entropies

    NASA Astrophysics Data System (ADS)

    Kirwan, A. D.

    2008-06-01

    Ecosystems and quantum gases share a number of superficial similarities including enormous numbers of interacting elements and the fundamental role of energy in such interactions. A theory for the synthesis of data and prediction of new phenomena is well established in quantum statistical mechanics. The premise of this paper is that the reason a comparable unifying theory has not emerged in ecology is that a proper role for entropy has yet to be assigned. To this end, a phase space entropy model of ecosystems is developed. Specification of an ecosystem phase space cell size based on microbial mass, length, and time scales gives an ecosystem uncertainty parameter only about three orders of magnitude larger than Planck’s constant. Ecosystem equilibria is specified by conservation of biomass and total metabolic energy, along with the principle of maximum entropy at equilibria. Both Bose - Einstein and Fermi - Dirac equilibrium conditions arise in ecosystems applications. The paper concludes with a discussion of some broader aspects of an ecosystem phase space.

  9. Entropy generation method to quantify thermal comfort

    NASA Technical Reports Server (NTRS)

    Boregowda, S. C.; Tiwari, S. N.; Chaturvedi, S. K.

    2001-01-01

    The present paper presents a thermodynamic approach to assess the quality of human-thermal environment interaction and quantify thermal comfort. The approach involves development of entropy generation term by applying second law of thermodynamics to the combined human-environment system. The entropy generation term combines both human thermal physiological responses and thermal environmental variables to provide an objective measure of thermal comfort. The original concepts and definitions form the basis for establishing the mathematical relationship between thermal comfort and entropy generation term. As a result of logic and deterministic approach, an Objective Thermal Comfort Index (OTCI) is defined and established as a function of entropy generation. In order to verify the entropy-based thermal comfort model, human thermal physiological responses due to changes in ambient conditions are simulated using a well established and validated human thermal model developed at the Institute of Environmental Research of Kansas State University (KSU). The finite element based KSU human thermal computer model is being utilized as a "Computational Environmental Chamber" to conduct series of simulations to examine the human thermal responses to different environmental conditions. The output from the simulation, which include human thermal responses and input data consisting of environmental conditions are fed into the thermal comfort model. Continuous monitoring of thermal comfort in comfortable and extreme environmental conditions is demonstrated. The Objective Thermal Comfort values obtained from the entropy-based model are validated against regression based Predicted Mean Vote (PMV) values. Using the corresponding air temperatures and vapor pressures that were used in the computer simulation in the regression equation generates the PMV values. The preliminary results indicate that the OTCI and PMV values correlate well under ideal conditions. However, an experimental study

  10. Self-organization and entropy reduction in a living cell

    PubMed Central

    Davies, Paul C.W.; Rieper, Elisabeth; Tuszynski, Jack A.

    2012-01-01

    In this paper we discuss the entropy and information aspects of a living cell. Particular attention is paid to the information gain on assembling and maintaining a living state. Numerical estimates of the information and entropy reduction are given and discussed in the context of the cell’s metabolic activity. We discuss a solution to an apparent paradox that there is less information content in DNA than in the proteins that are assembled based on the genetic code encrypted in DNA. When energy input required for protein synthesis is accounted for, the paradox is clearly resolved. Finally, differences between biological information and instruction are discussed. PMID:23159919

  11. Investigating dynamical complexity in the magnetosphere using various entropy measures

    NASA Astrophysics Data System (ADS)

    Balasis, Georgios; Daglis, Ioannis A.; Papadimitriou, Constantinos; Kalimeri, Maria; Anastasiadis, Anastasios; Eftaxias, Konstantinos

    2009-09-01

    The complex system of the Earth's magnetosphere corresponds to an open spatially extended nonequilibrium (input-output) dynamical system. The nonextensive Tsallis entropy has been recently introduced as an appropriate information measure to investigate dynamical complexity in the magnetosphere. The method has been employed for analyzing Dst time series and gave promising results, detecting the complexity dissimilarity among different physiological and pathological magnetospheric states (i.e., prestorm activity and intense magnetic storms, respectively). This paper explores the applicability and effectiveness of a variety of computable entropy measures (e.g., block entropy, Kolmogorov entropy, T complexity, and approximate entropy) to the investigation of dynamical complexity in the magnetosphere. We show that as the magnetic storm approaches there is clear evidence of significant lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with that inferred previously, from an independent linear fractal spectral analysis based on wavelet transforms. This convergence between nonlinear and linear analyses provides a more reliable detection of the transition from the quiet time to the storm time magnetosphere, thus showing evidence that the occurrence of an intense magnetic storm is imminent. More precisely, we claim that our results suggest an important principle: significant complexity decrease and accession of persistency in Dst time series can be confirmed as the magnetic storm approaches, which can be used as diagnostic tools for the magnetospheric injury (global instability). Overall, approximate entropy and Tsallis entropy yield superior results for detecting dynamical complexity changes in the magnetosphere in comparison to the other entropy measures presented herein. Ultimately, the analysis tools developed in the course of this study for the treatment of Dst index can provide convenience for space weather

  12. Entropy of electromyography time series

    NASA Astrophysics Data System (ADS)

    Kaufman, Miron; Zurcher, Ulrich; Sung, Paul S.

    2007-12-01

    A nonlinear analysis based on Renyi entropy is applied to electromyography (EMG) time series from back muscles. The time dependence of the entropy of the EMG signal exhibits a crossover from a subdiffusive regime at short times to a plateau at longer times. We argue that this behavior characterizes complex biological systems. The plateau value of the entropy can be used to differentiate between healthy and low back pain individuals.

  13. Entanglement Entropy of Black Holes

    NASA Astrophysics Data System (ADS)

    Solodukhin, Sergey N.

    2011-12-01

    The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ’t Hooft’s brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.

  14. Entanglement entropy on fuzzy spaces

    SciTech Connect

    Dou, Djamel; Ydri, Badis

    2006-08-15

    We study the entanglement entropy of a scalar field in 2+1 spacetime where space is modeled by a fuzzy sphere and a fuzzy disc. In both models we evaluate numerically the resulting entropies and find that they are proportional to the number of boundary degrees of freedom. In the Moyal plane limit of the fuzzy disc the entanglement entropy per unite area (length) diverges if the ignored region is of infinite size. The divergence is (interpreted) of IR-UV mixing origin. In general we expect the entanglement entropy per unite area to be finite on a noncommutative space if the ignored region is of finite size.

  15. Blog life: Entropy Bound

    NASA Astrophysics Data System (ADS)

    Steinberg, Peter

    2008-06-01

    Who is the blog written by? Peter Steinberg is a nuclear physicist at the Brookhaven National Laboratory in New York, US. He is acting project manager of the PHOBOS experiment, which used Brookhaven's Relativistic Heavy Ion Collider (RHIC) to search for unusual events produced during collisions between gold nuclei. He is also involved with the PHENIX experiment, which seeks to discover a new state of matter known as the quark-gluon plasma. In addition to his own blog Entropy Bound, Steinberg is currently blogging on a website that was set up last year to publicize the involvement of US scientists with the Large Hadron Collider (LHC) at CERN.

  16. Do `negative' temperatures exist?

    NASA Astrophysics Data System (ADS)

    Lavenda, B. H.

    1999-06-01

    A modification of the second law is required for a system with a bounded density of states and not the introduction of a `negative' temperature scale. The ascending and descending branches of the entropy versus energy curve describe particle and hole states, having thermal equations of state that are given by the Fermi and logistic distributions, respectively. Conservation of energy requires isentropic states to be isothermal. The effect of adiabatically reversing the field is entirely mechanical because the only difference between the two states is their energies. The laws of large and small numbers, leading to the normal and Poisson approximations, characterize statistically the states of infinite and zero temperatures, respectively. Since the heat capacity also vanishes in the state of maximum disorder, the third law can be generalized in systems with a bounded density of states: the entropy tends to a constant as the temperature tends to either zero or infinity.

  17. Order and correlation contributions to the entropy of hydrophobic solvation

    NASA Astrophysics Data System (ADS)

    Liu, Maoyuan; Besford, Quinn Alexander; Mulvaney, Thomas; Gray-Weale, Angus

    2015-03-01

    The entropy of hydrophobic solvation has been explained as the result of ordered solvation structures, of hydrogen bonds, of the small size of the water molecule, of dispersion forces, and of solvent density fluctuations. We report a new approach to the calculation of the entropy of hydrophobic solvation, along with tests of and comparisons to several other methods. The methods are assessed in the light of the available thermodynamic and spectroscopic information on the effects of temperature on hydrophobic solvation. Five model hydrophobes in SPC/E water give benchmark solvation entropies via Widom's test-particle insertion method, and other methods and models are tested against these particle-insertion results. Entropies associated with distributions of tetrahedral order, of electric field, and of solvent dipole orientations are examined. We find these contributions are small compared to the benchmark particle-insertion entropy. Competitive with or better than other theories in accuracy, but with no free parameters, is the new estimate of the entropy contributed by correlations between dipole moments. Dipole correlations account for most of the hydrophobic solvation entropy for all models studied and capture the distinctive temperature dependence seen in thermodynamic and spectroscopic experiments. Entropies based on pair and many-body correlations in number density approach the correct magnitudes but fail to describe temperature and size dependences, respectively. Hydrogen-bond definitions and free energies that best reproduce entropies from simulations are reported, but it is difficult to choose one hydrogen bond model that fits a variety of experiments. The use of information theory, scaled-particle theory, and related methods is discussed briefly. Our results provide a test of the Frank-Evans hypothesis that the negative solvation entropy is due to structured water near the solute, complement the spectroscopic detection of that solvation structure by

  18. Order and correlation contributions to the entropy of hydrophobic solvation

    SciTech Connect

    Liu, Maoyuan; Besford, Quinn Alexander; Mulvaney, Thomas; Gray-Weale, Angus

    2015-03-21

    The entropy of hydrophobic solvation has been explained as the result of ordered solvation structures, of hydrogen bonds, of the small size of the water molecule, of dispersion forces, and of solvent density fluctuations. We report a new approach to the calculation of the entropy of hydrophobic solvation, along with tests of and comparisons to several other methods. The methods are assessed in the light of the available thermodynamic and spectroscopic information on the effects of temperature on hydrophobic solvation. Five model hydrophobes in SPC/E water give benchmark solvation entropies via Widom’s test-particle insertion method, and other methods and models are tested against these particle-insertion results. Entropies associated with distributions of tetrahedral order, of electric field, and of solvent dipole orientations are examined. We find these contributions are small compared to the benchmark particle-insertion entropy. Competitive with or better than other theories in accuracy, but with no free parameters, is the new estimate of the entropy contributed by correlations between dipole moments. Dipole correlations account for most of the hydrophobic solvation entropy for all models studied and capture the distinctive temperature dependence seen in thermodynamic and spectroscopic experiments. Entropies based on pair and many-body correlations in number density approach the correct magnitudes but fail to describe temperature and size dependences, respectively. Hydrogen-bond definitions and free energies that best reproduce entropies from simulations are reported, but it is difficult to choose one hydrogen bond model that fits a variety of experiments. The use of information theory, scaled-particle theory, and related methods is discussed briefly. Our results provide a test of the Frank-Evans hypothesis that the negative solvation entropy is due to structured water near the solute, complement the spectroscopic detection of that solvation structure by

  19. Entropy and biological systems: Experimentally-investigated entropy-driven stacking of plant photosynthetic membranes

    PubMed Central

    Jia, Husen; Liggins, John R.; Chow, Wah Soon

    2014-01-01

    According to the Second Law of Thermodynamics, an overall increase of entropy contributes to the driving force for any physicochemical process, but entropy has seldom been investigated in biological systems. Here, for the first time, we apply Isothermal Titration Calorimetry (ITC) to investigate the Mg2+-induced spontaneous stacking of photosynthetic membranes isolated from spinach leaves. After subtracting a large endothermic interaction of MgCl2 with membranes, unrelated to stacking, we demonstrate that the enthalpy change (heat change at constant pressure) is zero or marginally positive or negative. This first direct experimental evidence strongly suggests that an entropy increase significantly drives membrane stacking in this ordered biological structure. Possible mechanisms for the entropy increase include: (i) the attraction between discrete oppositely-charged areas, releasing counterions; (ii) the release of loosely-bound water molecules from the inter-membrane gap; (iii) the increased orientational freedom of previously-aligned water dipoles; and (iv) the lateral rearrangement of membrane components. PMID:24561561

  20. Link Influence Entropy

    NASA Astrophysics Data System (ADS)

    Singh, Priti; Chakraborty, Abhishek; Manoj, B. S.

    2017-01-01

    In this paper we propose a new metric, Link Influence Entropy (LInE), which describes importance of each node based on the influence of each link present in a network. Influence of a link can neither be effectively estimated using betweenness centrality nor using degree based probability measures. The proposed LInE metric which provides an effective way to estimate the influence of a link in the network and incorporates this influence to identify nodal characteristics, performs better compared to degree based entropy. We found that LInE can differentiate various network types which degree-based or betweenness centrality based node influence metrics cannot. Our findings show that spatial wireless networks and regular grid networks, respectively, have lowest and highest LInE values. Finally, performance analysis of LInE is carried out on a real-world network as well as on a wireless mesh network testbed to study the influence of our metric as well as influence stability of nodes in dynamic networks.

  1. Macromolecular Entropy Can Be Accurately Computed from Force.

    PubMed

    Hensen, Ulf; Gräter, Frauke; Henchman, Richard H

    2014-11-11

    A method is presented to evaluate a molecule's entropy from the atomic forces calculated in a molecular dynamics simulation. Specifically, diagonalization of the mass-weighted force covariance matrix produces eigenvalues which in the harmonic approximation can be related to vibrational frequencies. The harmonic oscillator entropies of each vibrational mode may be summed to give the total entropy. The results for a series of hydrocarbons, dialanine and a β hairpin are found to agree much better with values derived from thermodynamic integration than results calculated using quasiharmonic analysis. Forces are found to follow a harmonic distribution more closely than coordinate displacements and better capture the underlying potential energy surface. The method's accuracy, simplicity, and computational similarity to quasiharmonic analysis, requiring as input force trajectories instead of coordinate trajectories, makes it readily applicable to a wide range of problems.

  2. Thermal expansion anomaly regulated by entropy.

    PubMed

    Liu, Zi-Kui; Wang, Yi; Shang, ShunLi

    2014-11-13

    Thermal expansion, defined as the temperature dependence of volume under constant pressure, is a common phenomenon in nature and originates from anharmonic lattice dynamics. However, it has been poorly understood how thermal expansion can show anomalies such as colossal positive, zero, or negative thermal expansion (CPTE, ZTE, or NTE), especially in quantitative terms. Here we show that changes in configurational entropy due to metastable micro(scopic)states can lead to quantitative prediction of these anomalies. We integrate the Maxwell relation, statistic mechanics, and first-principles calculations to demonstrate that when the entropy is increased by pressure, NTE occurs such as in Invar alloy (Fe3Pt, for example), silicon, ice, and water, and when the entropy is decreased dramatically by pressure, CPTE is expected such as in anti-Invar cerium, ice and water. Our findings provide a theoretic framework to understand and predict a broad range of anomalies in nature in addition to thermal expansion, which may include gigantic electrocaloric and electromechanical responses, anomalously reduced thermal conductivity, and spin distributions.

  3. Thermal Expansion Anomaly Regulated by Entropy

    PubMed Central

    Liu, Zi-Kui; Wang, Yi; Shang, ShunLi

    2014-01-01

    Thermal expansion, defined as the temperature dependence of volume under constant pressure, is a common phenomenon in nature and originates from anharmonic lattice dynamics. However, it has been poorly understood how thermal expansion can show anomalies such as colossal positive, zero, or negative thermal expansion (CPTE, ZTE, or NTE), especially in quantitative terms. Here we show that changes in configurational entropy due to metastable micro(scopic)states can lead to quantitative prediction of these anomalies. We integrate the Maxwell relation, statistic mechanics, and first-principles calculations to demonstrate that when the entropy is increased by pressure, NTE occurs such as in Invar alloy (Fe3Pt, for example), silicon, ice, and water, and when the entropy is decreased dramatically by pressure, CPTE is expected such as in anti-Invar cerium, ice and water. Our findings provide a theoretic framework to understand and predict a broad range of anomalies in nature in addition to thermal expansion, which may include gigantic electrocaloric and electromechanical responses, anomalously reduced thermal conductivity, and spin distributions. PMID:25391631

  4. Possible extended forms of thermodynamic entropy

    NASA Astrophysics Data System (ADS)

    Sasa, Shin-ichi

    2014-01-01

    Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon entropy of the microscopic degrees of freedom. Whenever an extension of thermodynamic entropy is attempted, we must pay special attention to how its three different aspects just mentioned are altered. In this paper, we discuss possible extensions of the thermodynamic entropy.

  5. Trajectory versus probability density entropy.

    PubMed

    Bologna, M; Grigolini, P; Karagiorgis, M; Rosa, A

    2001-07-01

    We show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. We adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the transport equation is built up for the purpose of affording a picture equivalent to that stemming from trajectory dynamics, no direct use of trajectory time evolution is allowed, once the transport equation is defined. With this definition in mind we prove that the detection of a time regime of increase of the density entropy with a rate identical to the KS entropy is possible only in a limited number of cases. The proposals made by some authors to establish a connection between the two entropies in general, violate our definition of density entropy and imply the concept of trajectory, which is foreign to that of density entropy.

  6. Configurational entropy of glueball states

    NASA Astrophysics Data System (ADS)

    Bernardini, Alex E.; Braga, Nelson R. F.; da Rocha, Roldão

    2017-02-01

    The configurational entropy of glueball states is calculated using a holographic description. Glueball states are represented by a supergravity dual picture, consisting of a 5-dimensional graviton-dilaton action of a dynamical holographic AdS/QCD model. The configurational entropy is studied as a function of the glueball spin and of the mass, providing information about the stability of the glueball states.

  7. Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Relative Entropy Distance and Energy Constraints

    NASA Astrophysics Data System (ADS)

    Winter, Andreas

    2016-10-01

    We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: first, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible form that depends only on the system dimension and the trace distance of the states. Almost the same proof can be used to derive similar continuity bounds for the relative entropy distance from a convex set of states or positive operators. As applications, we give new proofs, with tighter bounds, of the asymptotic continuity of the relative entropy of entanglement, E R , and its regularization {E_R^{∞}}, as well as of the entanglement of formation, E F . Using a novel "quantum coupling" of density operators, which may be of independent interest, we extend the latter to an asymptotic continuity bound for the regularized entanglement of formation, aka entanglement cost, {E_C=E_F^{∞}}. Second, we derive analogous continuity bounds for the von Neumann entropy and conditional entropy in infinite dimensional systems under an energy constraint, most importantly systems of multiple quantum harmonic oscillators. While without an energy bound the entropy is discontinuous, it is well-known to be continuous on states of bounded energy. However, a quantitative statement to that effect seems not to have been known. Here, under some regularity assumptions on the Hamiltonian, we find that, quite intuitively, the Gibbs entropy at the given energy roughly takes the role of the Hilbert space dimension in the finite-dimensional Fannes inequality.

  8. Revisiting sample entropy analysis

    NASA Astrophysics Data System (ADS)

    Govindan, R. B.; Wilson, J. D.; Eswaran, H.; Lowery, C. L.; Preißl, H.

    2007-03-01

    We modify the definition of sample entropy (SaEn) by incorporating a time delay between the components of the block (from which the densities are estimated) and show that the modified method characterizes the complexity of the system better than the original version. We apply the modified SaEn to the standard deterministic systems and stochastic processes (uncorrelated and long range correlated (LRC) processes) and show that the underlying complexity of the system is better quantified by the modified method. We extend this analysis to the RR intervals of the normal and congestive heart failure (CHF) subjects (available via www.physionet.org) and show that there is a good degree of separation between the two groups.

  9. FULL PARTICLE ELECTROMAGNETIC SIMULATIONS OF ENTROPY GENERATION ACROSS A COLLISIONLESS SHOCK

    SciTech Connect

    Yang, Zhongwei; Liu, Ying D.; Wang, Rui; Hu, Huidong; Parks, George K.; Wu, Pin; Huang, Can; Shi, Run

    2014-09-20

    Experimental data from Cluster have shown that entropy density can be generated across Earth's bow shock. These new observations are a starting point for a more sophisticated analysis that includes computer modeling of a collisionless shock using observed shock parameters as input. In this Letter, we present the first comparison between observations and particle-in-cell simulations of such entropy generation across a collisionless shock. The ion heating at the shock is dominated by the phase mixing of reflected and directly transmitted ions, which are separated from the incident ions. The electron heating is a nearly thermal process due to the conservation of their angular momentum. For both species, we calculate the entropy density across the shock, and obtain good consistency between observations and simulations on entropy generation across the shock. We also find that the entropy generation rate is reduced as the shock Mach number decreases.

  10. Bayes' estimators of generalized entropies

    NASA Astrophysics Data System (ADS)

    Holste, D.; Große, I.; Herzel, H.

    1998-03-01

    The order-q Tsallis 0305-4470/31/11/007/img5 and Rényi entropy 0305-4470/31/11/007/img6 receive broad applications in the statistical analysis of complex phenomena. A generic problem arises, however, when these entropies need to be estimated from observed data. The finite size of data sets can lead to serious systematic and statistical errors in numerical estimates. In this paper, we focus upon the problem of estimating generalized entropies from finite samples and derive the Bayes estimator of the order-q Tsallis entropy, including the order-1 (i.e. the Shannon) entropy, under the assumption of a uniform prior probability density. The Bayes estimator yields, in general, the smallest mean-quadratic deviation from the true parameter as compared with any other estimator. Exploiting the functional relationship between 0305-4470/31/11/007/img7 and 0305-4470/31/11/007/img8, we use the Bayes estimator of 0305-4470/31/11/007/img7 to estimate the Rényi entropy 0305-4470/31/11/007/img8. We compare these novel estimators with the frequency-count estimators for 0305-4470/31/11/007/img7 and 0305-4470/31/11/007/img8. We find by numerical simulations that the Bayes estimator reduces statistical errors of order-q entropy estimates for Bernoulli as well as for higher-order Markov processes derived from the complete genome of the prokaryote Haemophilus influenzae.

  11. Entanglement entropy converges to classical entropy around periodic orbits

    SciTech Connect

    Asplund, Curtis T.; Berenstein, David

    2016-03-15

    We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate the dependence of the entanglement entropy on the choice of coarse graining. We find that for almost all choices the asymptotic growth rate is the same.

  12. Nonequilibrium stationary states and entropy.

    PubMed

    Gallavotti, G; Cohen, E G D

    2004-03-01

    In transformations between nonequilibrium stationary states, entropy might not be a well defined concept. It might be analogous to the "heat content" in transformations in equilibrium which is not well defined either, if they are not isochoric (i.e., do involve mechanical work). Hence we conjecture that in a nonequilibrium stationary state the entropy is just a quantity that can be transferred or created, such as heat in equilibrium, but has no physical meaning as "entropy content" as a property of the system.

  13. Entropy distance: New quantum phenomena

    SciTech Connect

    Weis, Stephan; Knauf, Andreas

    2012-10-15

    We study a curve of Gibbsian families of complex 3 Multiplication-Sign 3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance, and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology, and information geometry. This research is motivated by a theory of infomax principles, where we contribute by computing first order optimality conditions of the entropy distance.

  14. Entropy in statistical energy analysis.

    PubMed

    Le Bot, Alain

    2009-03-01

    In this paper, the second principle of thermodynamics is discussed in the framework of statistical energy analysis (SEA). It is shown that the "vibrational entropy" and the "vibrational temperature" of sub-systems only depend on the vibrational energy and the number of resonant modes. A SEA system can be described as a thermodynamic system slightly out of equilibrium. In steady-state condition, the entropy exchanged with exterior by sources and dissipation exactly balances the production of entropy by irreversible processes at interface between SEA sub-systems.

  15. Entropy-as-a-Service: Unlocking the Full Potential of Cryptography

    PubMed Central

    Vassilev, Apostol; Staples, Robert

    2016-01-01

    Securing the Internet requires strong cryptography, which depends on the availability of good entropy for generating unpredictable keys and accurate clocks. Attacks abusing weak keys or old inputs portend challenges for the Internet. EaaS is a novel architecture providing entropy and timestamps from a decentralized root of trust, scaling gracefully across diverse geopolitical locales and remaining trustworthy unless much of the collective is compromised. PMID:28003687

  16. Entropy Production in Nonlinear, Thermally Driven Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Eckmann, Jean-Pierre; Pillet, Claude-Alain; Rey-Bellet, Luc

    1999-04-01

    We consider a finite chain of nonlinear oscillators coupled at its ends to two infinite heat baths which are at different temperatures. Using our earlier results about the existence of a stationary state, we show rigorously that for arbitrary temperature differences and arbitrary couplings, such a system has a unique stationary state. (This extends our earlier results for small temperature differences.) In all these cases, any initial state will converge (at an unknown rate) to the stationary state. We show that this stationary state continually produces entropy. The rate of entropy production is strictly negative when the temperatures are unequal and is proportional to the mean energy flux through the system

  17. Entropy exchange for infinite-dimensional systems

    PubMed Central

    Duan, Zhoubo; Hou, Jinchuan

    2017-01-01

    In this paper the entropy exchange for channels and states in infinite-dimensional systems are defined and studied. It is shown that, this entropy exchange depends only on the given channel and the state. An explicit expression of the entropy exchange in terms of the state and the channel is proposed. The generalized Klein’s inequality, the subadditivity and the triangle inequality about the entropy including infinite entropy for the infinite-dimensional systems are established, and then, applied to compare the entropy exchange with the entropy change. PMID:28164995

  18. High input impedance amplifier

    NASA Technical Reports Server (NTRS)

    Kleinberg, Leonard L.

    1995-01-01

    High input impedance amplifiers are provided which reduce the input impedance solely to a capacitive reactance, or, in a somewhat more complex design, provide an extremely high essentially infinite, capacitive reactance. In one embodiment, where the input impedance is reduced in essence, to solely a capacitive reactance, an operational amplifier in a follower configuration is driven at its non-inverting input and a resistor with a predetermined magnitude is connected between the inverting and non-inverting inputs. A second embodiment eliminates the capacitance from the input by adding a second stage to the first embodiment. The second stage is a second operational amplifier in a non-inverting gain-stage configuration where the output of the first follower stage drives the non-inverting input of the second stage and the output of the second stage is fed back to the non-inverting input of the first stage through a capacitor of a predetermined magnitude. These amplifiers, while generally useful, are very useful as sensor buffer amplifiers that may eliminate significant sources of error.

  19. MDS MIC Catalog Inputs

    NASA Technical Reports Server (NTRS)

    Johnson-Throop, Kathy A.; Vowell, C. W.; Smith, Byron; Darcy, Jeannette

    2006-01-01

    This viewgraph presentation reviews the inputs to the MDS Medical Information Communique (MIC) catalog. The purpose of the group is to provide input for updating the MDS MIC Catalog and to request that MMOP assign Action Item to other working groups and FSs to support the MITWG Process for developing MIC-DDs.

  20. Talking Speech Input.

    ERIC Educational Resources Information Center

    Berliss-Vincent, Jane; Whitford, Gigi

    2002-01-01

    This article presents both the factors involved in successful speech input use and the potential barriers that may suggest that other access technologies could be more appropriate for a given individual. Speech input options that are available are reviewed and strategies for optimizing use of speech recognition technology are discussed. (Contains…

  1. Orientational high-entropy alloys

    NASA Astrophysics Data System (ADS)

    Kumar, Nitesh; Subramaniam, Anandh

    2014-12-01

    In high-entropy alloys (HEA), the configurational entropy arising from the presence of multiple elements, stabilizes a disordered solid solution in preference to the possible formation of compounds. In the current work, we identify cluster compounds (of the type AM4X8) as orientational analogues of HEA (as a first report on orientational high-entropy systems). In cluster compounds, orientational disorder increases the entropy and plays a role analogous to positional disorder in HEA. In the GaMo4S8 compound, at temperatures greater than 50 K, the entropic benefit more than makes up for the strain energy cost and stabilizes the disordered phase in preference to an orientationally ordered compound.

  2. Quantum entropy and special relativity.

    PubMed

    Peres, Asher; Scudo, Petra F; Terno, Daniel R

    2002-06-10

    We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.

  3. An adaptable binary entropy coder

    NASA Technical Reports Server (NTRS)

    Kiely, A.; Klimesh, M.

    2001-01-01

    We present a novel entropy coding technique which is based on recursive interleaving of variable-to-variable length binary source codes. We discuss code design and performance estimation methods, as well as practical encoding and decoding algorithms.

  4. Entropy of Open Lattice Systems

    NASA Astrophysics Data System (ADS)

    Derrida, B.; Lebowitz, J. L.; Speer, E. R.

    2007-03-01

    We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in contact with particle reservoirs at different densities. In the hydrodynamic scaling limit, L → ∞, the leading order ( O( L)) behavior of this entropy has been shown by Bahadoran to be that of a product measure corresponding to strict local equilibrium; we compute the first correction, which is O(1). The computation uses a formal expansion of the entropy in terms of truncated correlation functions; for this system the k th such correlation is shown to be O( L - k+1). This entropy correction depends only on the scaled truncated pair correlation, which describes the covariance of the density field. It coincides, in the large L limit, with the corresponding correction obtained from a Gaussian measure with the same covariance.

  5. Dissipation, interaction, and relative entropy.

    PubMed

    Gaveau, B; Granger, L; Moreau, M; Schulman, L S

    2014-03-01

    Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (also called the Kullback-Leibler divergence). The processes considered are general time evolutions in both classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. As an application, the relative entropy is related to transport coefficients.

  6. Steganography Detection Using Entropy Measures

    DTIC Science & Technology

    2012-08-19

    REPORT Steganography Detection Using Entropy Measures 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: There are two problems in steganalysis: (1) detecting...the existence of a hidden message and (2) decoding the message. As terrorist groups have been known to use steganography in planning their attacks...298 (Rev 8/98) Prescribed by ANSI Std. Z39.18 - Steganography Detection Using Entropy Measures Report Title ABSTRACT There are two problems in

  7. Boundary effects in entanglement entropy

    NASA Astrophysics Data System (ADS)

    Berthiere, Clément; Solodukhin, Sergey N.

    2016-09-01

    We present a number of explicit calculations of Renyi and entanglement entropies in situations where the entangling surface intersects the boundary of d-dimensional Minkowski spacetime. When the boundary is a single plane we compute the contribution to the entropy due to this intersection, first in the case of the Neumann and Dirichlet boundary conditions, and then in the case of a generic Robin type boundary condition. The flow in the boundary coupling between the Neumann and Dirichlet phases is analyzed in arbitrary dimension d and is shown to be monotonic, the peculiarity of d = 3 case is noted. We argue that the translational symmetry along the entangling surface is broken due the presence of the boundary which reveals that the entanglement is not homogeneous. In order to characterize this quantitatively, we introduce a density of entanglement entropy and compute it explicitly. This quantity clearly indicates that the entanglement is maximal near the boundary. We then consider the situation where the boundary is composed of two parallel planes at a finite separation and compute the entanglement entropy as well as its density in this case. The complete contribution to entanglement entropy due to the boundaries is shown not to depend on the distance between the planes and is simply twice the entropy in the case of single plane boundary. Additionally, we find how the area law, the part in the entropy proportional to the area of entire entangling surface, depends on the size of the separation between the two boundaries. The latter is shown to appear in the UV finite part of the entropy.

  8. Information entropy to measure the spatial and temporal complexity of solute transport in heterogeneous porous media

    NASA Astrophysics Data System (ADS)

    Li, Weiyao; Huang, Guanhua; Xiong, Yunwu

    2016-04-01

    The complexity of the spatial structure of porous media, randomness of groundwater recharge and discharge (rainfall, runoff, etc.) has led to groundwater movement complexity, physical and chemical interaction between groundwater and porous media cause solute transport in the medium more complicated. An appropriate method to describe the complexity of features is essential when study on solute transport and conversion in porous media. Information entropy could measure uncertainty and disorder, therefore we attempted to investigate complexity, explore the contact between the information entropy and complexity of solute transport in heterogeneous porous media using information entropy theory. Based on Markov theory, two-dimensional stochastic field of hydraulic conductivity (K) was generated by transition probability. Flow and solute transport model were established under four conditions (instantaneous point source, continuous point source, instantaneous line source and continuous line source). The spatial and temporal complexity of solute transport process was characterized and evaluated using spatial moment and information entropy. Results indicated that the entropy increased as the increase of complexity of solute transport process. For the point source, the one-dimensional entropy of solute concentration increased at first and then decreased along X and Y directions. As time increased, entropy peak value basically unchanged, peak position migrated along the flow direction (X direction) and approximately coincided with the centroid position. With the increase of time, spatial variability and complexity of solute concentration increase, which result in the increases of the second-order spatial moment and the two-dimensional entropy. Information entropy of line source was higher than point source. Solute entropy obtained from continuous input was higher than instantaneous input. Due to the increase of average length of lithoface, media continuity increased, flow and

  9. Generalized Maximum Entropy

    NASA Technical Reports Server (NTRS)

    Cheeseman, Peter; Stutz, John

    2005-01-01

    A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this problem, advocated by E.T. Jaynes [1], is to ignore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic MaxEnt approach. Classic MaxEnt gives point probabilities (subject to the given constraints), rather than probability densities. We develop an alternative approach that assumes that the uncertain constraint values are represented by a probability density {e.g: a Gaussian), and this uncertainty yields a MaxEnt posterior probability density. That is, the classic MaxEnt point probabilities are regarded as a multidimensional function of the given constraint values, and uncertainty on these values is transmitted through the MaxEnt function to give uncertainty over the MaXEnt probabilities. We illustrate this approach by explicitly calculating the generalized MaxEnt density for a simple but common case, then show how this can be extended numerically to the general case. This paper expands the generalized MaxEnt concept introduced in a previous paper [3].

  10. Entropy Production and Fluctuation Relation in Turbulent Convection

    NASA Astrophysics Data System (ADS)

    Chibbaro, Sergio; Zonta, Francesco

    2016-11-01

    We report on a numerical experiment performed to analyze fluctuations of the entropy production in turbulent thermal convection. Using Direct Numerical Simulations (DNS), we estimate the entropy production from instantaneous measurements of the local temperature and velocity fields sampled along the trajectory of a large number of point-wise Lagrangian tracers. Entropy production is related to the work made by buoyancy force. The entropy production is characterized by large fluctuations and becomes often negative. This represents a sort of "finite-time" violation of the second principle of thermodynamics, since the direction of the energy flux is opposite to that prescribed by the external gradient. We provide a physical-sound definition of energy-scale characterizing the sytem, based upon Kolmogorov theory. Then, we link our results with recent theory of statistical mechanics of nonequilibrium systems, notably the results obtained by Evans, Cohen, Morris and Gallavotti for generic reversible dynamical systems. We show that the fluctuations of entropy production observed in the present system verify neatly the Fluctuation Relation (FR), cornerstone of that theory, even though the system is time-irreversible.

  11. Relative Entropy and Squashed Entanglement

    NASA Astrophysics Data System (ADS)

    Li, Ke; Winter, Andreas

    2014-02-01

    We are interested in the properties and relations of entanglement measures. Especially, we focus on the squashed entanglement and relative entropy of entanglement, as well as their analogues and variants. Our first result is a monogamy-like inequality involving the relative entropy of entanglement and its one-way LOCC variant. The proof is accomplished by exploring the properties of relative entropy in the context of hypothesis testing via one-way LOCC operations, and by making use of an argument resembling that by Piani on the faithfulness of regularized relative entropy of entanglement. Following this, we obtain a commensurate and faithful lower bound for squashed entanglement, in the form of one-way LOCC relative entropy of entanglement. This gives a strengthening to the strong subadditivity of von Neumann entropy. Our result improves the trace-distance-type bound derived in Brandão et al. (Commun Math Phys, 306:805-830, 2011), where faithfulness of squashed entanglement was first proved. Applying Pinsker's inequality, we are able to recover the trace-distance-type bound, even with slightly better constant factor. However, the main improvement is that our new lower bound can be much larger than the old one and it is almost a genuine entanglement measure. We evaluate exactly the relative entropy of entanglement under various restricted measurement classes, for maximally entangled states. Then, by proving asymptotic continuity, we extend the exact evaluation to their regularized versions for all pure states. Finally, we consider comparisons and separations between some important entanglement measures and obtain several new results on these, too.

  12. Classification of 5-S Epileptic EEG Recordings Using Distribution Entropy and Sample Entropy.

    PubMed

    Li, Peng; Karmakar, Chandan; Yan, Chang; Palaniswami, Marimuthu; Liu, Changchun

    2016-01-01

    Epilepsy is an electrophysiological disorder of the brain, the hallmark of which is recurrent and unprovoked seizures. Electroencephalogram (EEG) measures electrical activity of the brain that is commonly applied as a non-invasive technique for seizure detection. Although a vast number of publications have been published on intelligent algorithms to classify interictal and ictal EEG, it remains an open question whether they can be detected using short-length EEG recordings. In this study, we proposed three protocols to select 5 s EEG segment for classifying interictal and ictal EEG from normal. We used the publicly-accessible Bonn database, which consists of normal, interical, and ictal EEG signals with a length of 4097 sampling points (23.6 s) per record. In this study, we selected three segments of 868 points (5 s) length from each recordings and evaluated results for each of them separately. The well-studied irregularity measure-sample entropy (SampEn)-and a more recently proposed complexity measure-distribution entropy (DistEn)-were used as classification features. A total of 20 combinations of input parameters m and τ for the calculation of SampEn and DistEn were selected for compatibility. Results showed that SampEn was undefined for half of the used combinations of input parameters and indicated a large intra-class variance. Moreover, DistEn performed robustly for short-length EEG data indicating relative independence from input parameters and small intra-class fluctuations. In addition, it showed acceptable performance for all three classification problems (interictal EEG from normal, ictal EEG from normal, and ictal EEG from interictal) compared to SampEn, which showed better results only for distinguishing normal EEG from interictal and ictal. Both SampEn and DistEn showed good reproducibility and consistency, as evidenced by the independence of results on analysing protocol.

  13. Some new measures of entropy, useful tools in biocomputing.

    PubMed

    Garrido, Angel

    2010-01-01

    The basic problem rooted in Information Theory (IT) foundations (Shannon, Bell Syst Tech J 27:379-423 and 623-656, 1948; Volkenstein, Entropy and Information. Series: Progress in Mathematical Physics, 2009) is to reconstruct, as closely as possible, the input signal after observing the received output signal.The Shannon information measure is the only possible one in this context, but it must be clear that it is only valid within the more restricted scope of coding problems that C. E. Shannon himself had seen in his lifetime (Shannon, Bell Syst Tech J 27:379-423 and 623-656, 1948). As pointed out by Alfred Rényi (1961), in his essential paper (Rényi, Proc. of the 4th Berkeley Symposium on Mathematics, Statistics and Probability, 547-561, 1961) on generalized information measures, for other sorts of problems other quantities may serve just as well as measures of information, or even better. This would be supported either by their operational significance or by a set of natural postulates characterizing them, or preferably by both. Thus, the idea of generalized entropies arises in scientific literature.We analyze here some new measures of Entropy, very useful to be applied on Biocomputing (Ulanowicz and Hannon, Proc R Soc Lond B 232:181-192, 1987; Volkenstein, Entropy and Information. Series: Progress in Mathematical Physics, 2009).

  14. Wavelet entropy of stochastic processes

    NASA Astrophysics Data System (ADS)

    Zunino, L.; Pérez, D. G.; Garavaglia, M.; Rosso, O. A.

    2007-06-01

    We compare two different definitions for the wavelet entropy associated to stochastic processes. The first one, the normalized total wavelet entropy (NTWS) family [S. Blanco, A. Figliola, R.Q. Quiroga, O.A. Rosso, E. Serrano, Time-frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function, Phys. Rev. E 57 (1998) 932-940; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals, J. Neurosci. Method 105 (2001) 65-75] and a second introduced by Tavares and Lucena [Physica A 357(1) (2005) 71-78]. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise ( -1<α< 1) and fractional Brownian motion ( 1<α< 3) are assessed. We find out that the NTWS family performs better as a characterization method for these stochastic processes.

  15. Quantum geometry and gravitational entropy

    SciTech Connect

    Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan

    2007-05-29

    Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.

  16. Conditional entropy and Landauer principle

    NASA Astrophysics Data System (ADS)

    Chiuchiú, D.; Diamantini, M. C.; Gammaitoni, L.

    2015-08-01

    The Landauer principle describes the minimum heat produced by an information-processing device. Recently a new term has been included in the minimum heat production: it is called conditional entropy and takes into account the microstates content of a given logic state. Usually this term is assumed to be zero in bistable symmetric systems thanks to the strong hypothesis used to derive the Landauer principle. In this paper we show that conditional entropy can be nonzero even for bistable symmetric systems and that it can be expressed as the sum of three different terms related to the probabilistic features of the device. The contribution of the three terms to conditional entropy (and thus to the minimum heat production) is then discussed for the case of bit reset.

  17. Convex Accelerated Maximum Entropy Reconstruction

    PubMed Central

    Worley, Bradley

    2016-01-01

    Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm – called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm – is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra. PMID:26894476

  18. Input and Input Processing in Second Language Acquisition.

    ERIC Educational Resources Information Center

    Alcon, Eva

    1998-01-01

    Analyzes second-language learners' processing of linguistic data within the target language, focusing on input and intake in second-language acquisition and factors and cognitive processes that affect input processing. Input factors include input simplification, input enhancement, and interactional modifications. Individual learner differences…

  19. Input Decimated Ensembles

    NASA Technical Reports Server (NTRS)

    Tumer, Kagan; Oza, Nikunj C.; Clancy, Daniel (Technical Monitor)

    2001-01-01

    Using an ensemble of classifiers instead of a single classifier has been shown to improve generalization performance in many pattern recognition problems. However, the extent of such improvement depends greatly on the amount of correlation among the errors of the base classifiers. Therefore, reducing those correlations while keeping the classifiers' performance levels high is an important area of research. In this article, we explore input decimation (ID), a method which selects feature subsets for their ability to discriminate among the classes and uses them to decouple the base classifiers. We provide a summary of the theoretical benefits of correlation reduction, along with results of our method on two underwater sonar data sets, three benchmarks from the Probenl/UCI repositories, and two synthetic data sets. The results indicate that input decimated ensembles (IDEs) outperform ensembles whose base classifiers use all the input features; randomly selected subsets of features; and features created using principal components analysis, on a wide range of domains.

  20. Localization of negative energy and the Bekenstein bound.

    PubMed

    Blanco, David D; Casini, Horacio

    2013-11-27

    A simple argument shows that negative energy cannot be isolated far away from positive energy in a conformal field theory and strongly constrains its possible dispersal. This is also required by consistency with the Bekenstein bound written in terms of the positivity of relative entropy. We prove a new form of the Bekenstein bound based on the monotonicity of the relative entropy, involving a "free" entropy enclosed in a region which is highly insensitive to space-time entanglement, and show that it further improves the negative energy localization bound.

  1. The Effect of Input-Based Instruction Type on the Acquisition of Spanish Accusative Clitics

    ERIC Educational Resources Information Center

    White, Justin

    2015-01-01

    The purpose of this paper is to compare structured input (SI) with other input-based instructional treatments. The input-based instructional types include: input flood (IF), text enhancement (TE), SI activities, and focused input (FI; SI without implicit negative feedback). Participants included 145 adult learners enrolled in an intermediate…

  2. Using entropy measures to characterize human locomotion.

    PubMed

    Leverick, Graham; Szturm, Tony; Wu, Christine Q

    2014-12-01

    Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this paper, the value of using entropy measures to characterize human locomotion is demonstrated based on their construct validity, predictive validity in a simple model of human walking and convergent validity in an experimental study. Results show that four of the five considered entropy measures increase meaningfully with the increased probability of falling in a simple passive bipedal walker model. The same four entropy measures also experienced statistically significant increases in response to increasing age and gait impairment caused by cognitive interference in an experimental study. Of the considered entropy measures, the proposed quantized dynamical entropy (QDE) and quantization-based approximation of sample entropy (QASE) offered the best combination of sensitivity to changes in gait dynamics and computational efficiency. Based on these results, entropy appears to be a viable candidate for assessing the stability of human locomotion.

  3. Entropy Analyses of Four Familiar Processes.

    ERIC Educational Resources Information Center

    Craig, Norman C.

    1988-01-01

    Presents entropy analysis of four processes: a chemical reaction, a heat engine, the dissolution of a solid, and osmosis. Discusses entropy, the second law of thermodynamics, and the Gibbs free energy function. (MVL)

  4. Entropy of a vacuum: What does the covariant entropy count?

    NASA Astrophysics Data System (ADS)

    Nomura, Yasunori; Weinberg, Sean J.

    2014-11-01

    We argue that a unitary description of the formation and evaporation of a black hole implies that the Bekenstein-Hawking entropy is the "entropy of a vacuum": the logarithm of the number of possible independent ways in which quantum field theory on a fixed classical spacetime background can emerge in a full quantum theory of gravity. In many cases, the covariant entropy counts this entropy—the degeneracy of emergent quantum field theories in full quantum gravity—with the entropy of particle excitations in each quantum field theory giving only a tiny perturbation. In the Rindler description of a (black hole) horizon, the relevant vacuum degrees of freedom manifest themselves as an extra hidden quantum number carried by the states representing the second exterior region; this quantum number is invisible in the emergent quantum field theory. In a distant picture, these states arise as exponentially degenerate ground and excited states of the intrinsically quantum gravitational degrees of freedom on the stretched horizon. The formation and evaporation of a black hole involve processes in which the entropy of collapsing matter is transformed into that of a vacuum and then to that of final-state Hawking radiation. In the intermediate stage of this evolution, entanglement between the vacuum and (early) Hawking radiation develops, which is transferred to the entanglement among final-state Hawking quanta through the evaporation process. The horizon is kept smooth throughout the evolution; in particular, no firewall develops. Similar considerations also apply for cosmological horizons, for example for the horizon of a metastable de Sitter space.

  5. Tachyon condensation and black hole entropy.

    PubMed

    Dabholkar, Atish

    2002-03-04

    String propagation on a cone with deficit angle 2pi(1-1 / N) is considered for the purpose of computing the entropy of a large mass black hole. The entropy computed using the recent results on condensation of twisted-sector tachyons in this theory is found to be in precise agreement with the Bekenstein-Hawking entropy.

  6. Entropy and temperatures of Nariai black hole

    NASA Astrophysics Data System (ADS)

    Eune, Myungseok; Kim, Wontae

    2013-06-01

    The statistical entropy of the Nariai black hole in a thermal equilibrium is calculated by using the brick-wall method. Even if the temperature depends on the choice of the timelike Killing vector, the entropy can be written by the ordinary area law which agrees with the Wald entropy. We discuss some physical consequences of this result and the properties of the temperatures.

  7. Remainder terms for some quantum entropy inequalities

    SciTech Connect

    Carlen, Eric A.; Lieb, Elliott H.

    2014-04-15

    We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy. For these we state conditions for equality, and we prove some new error bounds away from equality, including an improved version of Pinsker's inequality.

  8. Coherent Informational Energy and Entropy.

    ERIC Educational Resources Information Center

    Avramescu, Aurel

    1980-01-01

    Seeks to provide a common theoretical foundation for all known bibliometric laws by assimilating a systemic view of the information transfer process with a thermodynamic process, i.e., the conduction of heat in solids. The resulting diffusion model establishes new definitions for informational energy and entropy consistent with corresponding…

  9. Numerical calculation of granular entropy.

    PubMed

    Asenjo, Daniel; Paillusson, Fabien; Frenkel, Daan

    2014-03-07

    We present numerical simulations that allow us to compute the number of ways in which N particles can pack into a given volume V. Our technique modifies the method of Xu, Frenkel, and Liu [Phys. Rev. Lett. 106, 245502 (2011)] and outperforms existing direct enumeration methods by more than 200 orders of magnitude. We use our approach to study the system size dependence of the number of distinct packings of a system of up to 128 polydisperse soft disks. We show that, even though granular particles are distinguishable, we have to include a factor 1=N! to ensure that the entropy does not change when exchanging particles between systems in the same macroscopic state. Our simulations provide strong evidence that the packing entropy, when properly defined, is extensive. As different packings are created with unequal probabilities, it is natural to express the packing entropy as S = − Σ(i)p(i) ln pi − lnN!, where pi denotes the probability to generate the ith packing. We can compute this quantity reliably and it is also extensive. The granular entropy thus (re)defined, while distinct from the one proposed by Edwards [J. Phys. Condens. Matter 2, SA63 (1990)], does have all the properties Edwards assumed.

  10. Numerical Calculation of Granular Entropy

    NASA Astrophysics Data System (ADS)

    Asenjo, Daniel; Paillusson, Fabien; Frenkel, Daan

    2014-03-01

    We present numerical simulations that allow us to compute the number of ways in which N particles can pack into a given volume V. Our technique modifies the method of Xu, Frenkel, and Liu [Phys. Rev. Lett. 106, 245502 (2011)] and outperforms existing direct enumeration methods by more than 200 orders of magnitude. We use our approach to study the system size dependence of the number of distinct packings of a system of up to 128 polydisperse soft disks. We show that, even though granular particles are distinguishable, we have to include a factor 1/N! to ensure that the entropy does not change when exchanging particles between systems in the same macroscopic state. Our simulations provide strong evidence that the packing entropy, when properly defined, is extensive. As different packings are created with unequal probabilities, it is natural to express the packing entropy as S=-∑ipilnpi-lnN!, where pi denotes the probability to generate the ith packing. We can compute this quantity reliably and it is also extensive. The granular entropy thus (re)defined, while distinct from the one proposed by Edwards [J. Phys. Condens. Matter 2, SA63 (1990)], does have all the properties Edwards assumed.

  11. Holographic entropy and Calabi's diastasis

    NASA Astrophysics Data System (ADS)

    D'Hoker, Eric; Gutperle, Michael

    2014-10-01

    The entanglement entropy for interfaces and junctions of two-dimensional CFTs is evaluated on holographically dual half-BPS solutions to six-dimensional Type 4b supergravity with m anti-symmetric tensor supermultiplets. It is shown that the moduli space for an N-junction solution projects to N points in the Kähler manifold SO(2 , m) / (SO(2) × SO( m)). For N =2 the interface entropy is expressed in terms of the central charge and Calabi's diastasis function on SO(2 , m) / (SO(2) × SO( m)), thereby lending support from holography to a proposal of Bachas, Brunner, Douglas, and Rastelli. For N =3, the entanglement entropy for a 3-junction decomposes into a sum of diastasis functions between pairs, weighed by combinations of the three central charges, provided the flux charges are all parallel to one another or, more generally, provided the space of flux charges is orthogonal to the space of unattracted scalars. Under similar assumptions for N ≥4, the entanglement entropy for the N -junction solves a variational problem whose data consist of the N central charges, and the diastasis function evaluated between pairs of N asymptotic AdS 3 × S 3 regions.

  12. Origin of the 'Extra Entropy'

    NASA Technical Reports Server (NTRS)

    Mushotzky, R.

    2008-01-01

    I will discuss how one can determine the origin of the 'extra entropy' in groups and clusters and the feedback needed in models of galaxy formation. I will stress the use of x-ray spectroscopy and imaging and the critical value that Con-X has in this regard.

  13. Entropy in an expanding universe

    NASA Astrophysics Data System (ADS)

    Frautschi, S.

    1982-08-01

    The evolution of organized structures from initial chaos in the expanding universe is demonstrated to be reconcilable with the second law of thermodynamics, and the effects of expansion and gravity on this problem are emphasized. Numerical estimates of the major sources of entropy increase are calculated, including the entropy increase in stars, the earth, black hole formation and decay, quantum tunneling of matter into black holes, positronium formation and decay, etc. An expanding 'causal' region is defined in which the entropy, though increasing, tends to fall further and further behind its maximum possible value, thus allowing for the development of order. That is, the classical heat death argument does not hold, because an expanding universe never achieves equilibrium and never reaches a constant temperature. Also considered are questions of whether entropy will continue increasing without limit in the future, and whether such increase in the form of Hawking radiation or radiation from positronium might enable life to maintain itself permanently. Attempts to find a scheme for preserving life based on solid structures fail because events such as quantum tunneling recurrently disorganize matter on a very long but fixed time scale.

  14. Entanglement entropy and anomaly inflow

    NASA Astrophysics Data System (ADS)

    Hughes, Taylor L.; Leigh, Robert G.; Parrikar, Onkar; Ramamurthy, Srinidhi T.

    2016-03-01

    We study entanglement entropy for parity-violating (time-reversal breaking) quantum field theories on R1 ,2 in the presence of a domain wall between two distinct parity-odd phases. The domain wall hosts a 1 +1 -dimensional conformal field theory (CFT) with nontrivial chiral central charge. Such a CFT possesses gravitational anomalies. It has been shown recently that, as a consequence, its intrinsic entanglement entropy is sensitive to Lorentz boosts around the entangling surface. Here, we show using various methods that the entanglement entropy of the three-dimensional bulk theory is also sensitive to such boosts owing to parity-violating effects, and that the bulk response to a Lorentz boost precisely cancels the contribution coming from the domain wall CFT. We argue that this can naturally be interpreted as entanglement inflow (i.e., inflow of entanglement entropy analogous to the familiar Callan-Harvey effect) between the bulk and the domain-wall, mediated by the low-lying states in the entanglement spectrum. These results can be generally applied to 2 +1 -d topological phases of matter that have edge theories with gravitational anomalies, and provide a precise connection between the gravitational anomaly of the physical edge theory and the low-lying spectrum of the entanglement Hamiltonian.

  15. Entropy, semantic relatedness and proximity.

    PubMed

    Hahn, Lance W; Sivley, Robert M

    2011-09-01

    Although word co-occurrences within a document have been demonstrated to be semantically useful, word interactions over a local range have been largely neglected by psychologists due to practical challenges. Shannon's (Bell Systems Technical Journal, 27, 379-423, 623-665, 1948) conceptualization of information theory suggests that these interactions should be useful for understanding communication. Computational advances make an examination of local word-word interactions possible for a large text corpus. We used Brants and Franz's (2006) dataset to generate conditional probabilities for 62,474 word pairs and entropy calculations for 9,917 words in Nelson, McEvoy, and Schreiber's (Behavior Research Methods, Instruments, & Computers, 36, 402-407, 2004) free association norms. Semantic associativity correlated moderately with the probabilities and was stronger when the two words were not adjacent. The number of semantic associates for a word and the entropy of a word were also correlated. Finally, language entropy decreases from 11 bits for single words to 6 bits per word for four-word sequences. The probabilities and entropies discussed here are included in the supplemental materials for the article.

  16. Entropy: A new measure of stock market volatility?

    NASA Astrophysics Data System (ADS)

    Bentes, Sonia R.; Menezes, Rui

    2012-11-01

    When uncertainty dominates understanding stock market volatility is vital. There are a number of reasons for that. On one hand, substantial changes in volatility of financial market returns are capable of having significant negative effects on risk averse investors. In addition, such changes can also impact on consumption patterns, corporate capital investment decisions and macroeconomic variables. Arguably, volatility is one of the most important concepts in the whole finance theory. In the traditional approach this phenomenon has been addressed based on the concept of standard-deviation (or variance) from which all the famous ARCH type models - Autoregressive Conditional Heteroskedasticity Models- depart. In this context, volatility is often used to describe dispersion from an expected value, price or model. The variability of traded prices from their sample mean is only an example. Although as a measure of uncertainty and risk standard-deviation is very popular since it is simple and easy to calculate it has long been recognized that it is not fully satisfactory. The main reason for that lies in the fact that it is severely affected by extreme values. This may suggest that this is not a closed issue. Bearing on the above we might conclude that many other questions might arise while addressing this subject. One of outstanding importance, from which more sophisticated analysis can be carried out, is how to evaluate volatility, after all? If the standard-deviation has some drawbacks shall we still rely on it? Shall we look for an alternative measure? In searching for this shall we consider the insight of other domains of knowledge? In this paper we specifically address if the concept of entropy, originally developed in physics by Clausius in the XIX century, which can constitute an effective alternative. Basically, what we try to understand is, which are the potentialities of entropy compared to the standard deviation. But why entropy? The answer lies on the fact

  17. Maximum entropy principle and partial probability weighted moments

    NASA Astrophysics Data System (ADS)

    Deng, Jian; Pandey, M. D.; Xie, W. C.

    2012-05-01

    Maximum entropy principle (MaxEnt) is usually used for estimating the probability density function under specified moment constraints. The density function is then integrated to obtain the cumulative distribution function, which needs to be inverted to obtain a quantile corresponding to some specified probability. In such analysis, consideration of higher ordermoments is important for accurate modelling of the distribution tail. There are three drawbacks for this conventional methodology: (1) Estimates of higher order (>2) moments from a small sample of data tend to be highly biased; (2) It can merely cope with problems with complete or noncensored samples; (3) Only probability weighted moments of integer orders have been utilized. These difficulties inevitably induce bias and inaccuracy of the resultant quantile estimates and therefore have been the main impediments to the application of the MaxEnt Principle in extreme quantile estimation. This paper attempts to overcome these problems and presents a distribution free method for estimating the quantile function of a non-negative randomvariable using the principle of maximum partial entropy subject to constraints of the partial probability weighted moments estimated from censored sample. The main contributions include: (1) New concepts, i.e., partial entropy, fractional partial probability weighted moments, and partial Kullback-Leibler measure are elegantly defined; (2) Maximum entropy principle is re-formulated to be constrained by fractional partial probability weighted moments; (3) New distribution free quantile functions are derived. Numerical analyses are performed to assess the accuracy of extreme value estimates computed from censored samples.

  18. Thai Negation.

    ERIC Educational Resources Information Center

    Alam, Samsul

    A study analyzed the structure of negative sentences in the Thai language, based on data gathered from two native speakers. It is shown that the Thai negative marker generally occurs between the noun phrase (subject) and the verb phrase in simple active sentences and in passive sentences. Negation of noun phrases is also allowed in Thai, with a…

  19. Time evolution of entropy in gravitational collapse

    SciTech Connect

    Greenwood, Eric

    2009-06-01

    We study the time evolution of the entropy of a collapsing spherical domain wall, from the point of view of an asymptotic observer, by investigating the entropy of the entire system (i.e. domain wall and radiation) and induced radiation alone during the collapse. By taking the difference, we find the entropy of the collapsing domain wall, since this is the object which will form a black hole. We find that for large values of time (times larger than t/R{sub s} ≈ 8), the entropy of the collapsing domain wall is a constant, which is of the same order as the Bekenstein-Hawking entropy.

  20. Controlling the shannon entropy of quantum systems.

    PubMed

    Xing, Yifan; Wu, Jun

    2013-01-01

    This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

  1. q-entropy for symbolic dynamical systems

    NASA Astrophysics Data System (ADS)

    Zhao, Yun; Pesin, Yakov

    2015-12-01

    For symbolic dynamical systems we use the Carathéodory construction as described in (Pesin 1997 Dimension Theory in Dynamical Systems, ConTemporary Views and Applications (Chicago: University of Chicago Press)) to introduce the notions of q-topological and q-metric entropies. We describe some basic properties of these entropies and in particular, discuss relations between q-metric entropy and local metric entropy. Both q-topological and q-metric entropies are new invariants respectively under homeomorphisms and metric isomorphisms of dynamical systems.

  2. Entropy-based portfolio models: Practical issues

    NASA Astrophysics Data System (ADS)

    Shirazi, Yasaman Izadparast; Sabiruzzaman, Md.; Hamzah, Nor Aishah

    2015-10-01

    Entropy is a nonparametric alternative of variance and has been used as a measure of risk in portfolio analysis. In this paper, the computation of entropy risk for a given set of data is discussed with illustration. A comparison between entropy-based portfolio models is made. We propose a natural extension of the mean entropy portfolio to make it more general and diversified. In terms of performance, this new model is similar to the mean-entropy portfolio when applied to real and simulated data, and offers higher return if no constraint is set for the desired return; also it is found to be the most diversified portfolio model.

  3. Tsallis Entropy Composition and the Heisenberg Group

    NASA Astrophysics Data System (ADS)

    Kalogeropoulos, Nikos

    2013-03-01

    We present an embedding of the Tsallis entropy into the three-dimensional Heisenberg group, in order to understand the meaning of generalized independence as encoded in the Tsallis entropy composition property. We infer that the Tsallis entropy composition induces fractal properties on the underlying Euclidean space. Using a theorem of Milnor/Wolf/Tits/Gromov, we justify why the underlying configuration/phase space of systems described by the Tsallis entropy has polynomial growth for both discrete and Riemannian cases. We provide a geometric framework that elucidates Abe's formula for the Tsallis entropy, in terms the Pansu derivative of a map between sub-Riemannian spaces.

  4. Generalized gravitational entropy from total derivative action

    NASA Astrophysics Data System (ADS)

    Dong, Xi; Miao, Rong-Xin

    2015-12-01

    We investigate the generalized gravitational entropy from total derivative terms in the gravitational action. Following the method of Lewkowycz and Maldacena, we find that the generalized gravitational entropy from total derivatives vanishes. We compare our results with the work of Astaneh, Patrushev, and Solodukhin. We find that if total derivatives produced nonzero entropy, the holographic and the field-theoretic universal terms of entanglement entropy would not match. Furthermore, the second law of thermodynamics could be violated if the entropy of total derivatives did not vanish.

  5. Nonparametric entropy estimation using kernel densities.

    PubMed

    Lake, Douglas E

    2009-01-01

    The entropy of experimental data from the biological and medical sciences provides additional information over summary statistics. Calculating entropy involves estimates of probability density functions, which can be effectively accomplished using kernel density methods. Kernel density estimation has been widely studied and a univariate implementation is readily available in MATLAB. The traditional definition of Shannon entropy is part of a larger family of statistics, called Renyi entropy, which are useful in applications that require a measure of the Gaussianity of data. Of particular note is the quadratic entropy which is related to the Friedman-Tukey (FT) index, a widely used measure in the statistical community. One application where quadratic entropy is very useful is the detection of abnormal cardiac rhythms, such as atrial fibrillation (AF). Asymptotic and exact small-sample results for optimal bandwidth and kernel selection to estimate the FT index are presented and lead to improved methods for entropy estimation.

  6. Entropy Generation Across Earth's Bow Shock

    NASA Technical Reports Server (NTRS)

    Parks, George K.; McCarthy, Michael; Fu, Suiyan; Lee E. s; Cao, Jinbin; Goldstein, Melvyn L.; Canu, Patrick; Dandouras, Iannis S.; Reme, Henri; Fazakerley, Andrew; Lin, Naiguo; Wilber, Mark

    2011-01-01

    Earth's bow shock is a transition layer that causes an irreversible change in the state of plasma that is stationary in time. Theories predict entropy increases across the bow shock but entropy has never been directly measured. Cluster and Double Star plasma experiments measure 3D plasma distributions upstream and downstream of the bow shock that allow calculation of Boltzmann's entropy function H and his famous H-theorem, dH/dt O. We present the first direct measurements of entropy density changes across Earth's bow shock. We will show that this entropy generation may be part of the processes that produce the non-thermal plasma distributions is consistent with a kinetic entropy flux model derived from the collisionless Boltzmann equation, giving strong support that solar wind's total entropy across the bow shock remains unchanged. As far as we know, our results are not explained by any existing shock models and should be of interests to theorists.

  7. Entropy-based financial asset pricing.

    PubMed

    Ormos, Mihály; Zibriczky, Dávid

    2014-01-01

    We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

  8. Entropy-Based Financial Asset Pricing

    PubMed Central

    Ormos, Mihály; Zibriczky, Dávid

    2014-01-01

    We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return – entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy. PMID:25545668

  9. Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

    NASA Astrophysics Data System (ADS)

    Tsukiji, Hidekazu; Iida, Hideaki; Kunihiro, Teiji; Ohnishi, Akira; Takahashi, Toru T.

    2016-11-01

    We investigate possible entropy production in Yang-Mills (YM) field theory by using a quantum distribution function called the Husimi function fH(A ,E ,t ) for the YM field, which is given by a coarse graining of the Wigner function and non-negative. We calculate the Husimi-Wehrl entropy SHW(t )=-Tr fHlog fH defined as an integral over the phase space, for which two adaptations of the test-particle method are used combined with Monte Carlo method. We utilize the semiclassical approximation to obtain the time evolution of the distribution functions of the YM field, which is known to show chaotic behavior in the classical limit. We also make a simplification of the multidimensional phase-space integrals by making a product ansatz for the Husimi function, which is found to give a 10-20% overestimate of the Husimi-Wehrl entropy for a quantum system with a few degrees of freedom. We show that the quantum YM theory does exhibit the entropy production and that the entropy production rate agrees with the sum of positive Lyapunov exponents or the Kolmogorov-Sinai entropy, suggesting that the chaoticity of the classical YM field causes the entropy production in the quantum YM theory.

  10. Entanglement entropy production in gravitational collapse: covariant regularization and solvable models

    NASA Astrophysics Data System (ADS)

    Bianchi, Eugenio; De Lorenzo, Tommaso; Smerlak, Matteo

    2015-06-01

    We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that ( i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, ( ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, ( iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.

  11. Bacterial chemotaxis and entropy production

    PubMed Central

    Županović, Paško; Brumen, Milan; Jagodič, Marko; Juretić, Davor

    2010-01-01

    Entropy production is calculated for bacterial chemotaxis in the case of a migrating band of bacteria in a capillary tube. It is found that the speed of the migrating band is a decreasing function of the starting concentration of the metabolizable attractant. The experimentally found dependence of speed on the starting concentration of galactose, glucose and oxygen is fitted with power-law functions. It is found that the corresponding exponents lie within the theoretically predicted interval. The effect of the reproduction of bacteria on band speed is considered, too. The acceleration of the band is predicted due to the reproduction rate of bacteria. The relationship between chemotaxis, the maximum entropy production principle and the formation of self-organizing structure is discussed. PMID:20368258

  12. Manufacturing of High Entropy Alloys

    NASA Astrophysics Data System (ADS)

    Jablonski, Paul D.; Licavoli, Joseph J.; Gao, Michael C.; Hawk, Jeffrey A.

    2015-07-01

    High entropy alloys (HEAs) have generated interest in recent years due to their unique positioning within the alloy world. By incorporating a number of elements in high proportion they have high configurational entropy, and thus they hold the promise of interesting and useful properties such as enhanced strength and phase stability. The present study investigates the microstructure of two single-phase face-centered cubic (FCC) HEAs, CoCrFeNi and CoCrFeNiMn, with special attention given to melting, homogenization and thermo-mechanical processing. Large-scale ingots were made by vacuum induction melting to avoid the extrinsic factors inherent in small-scale laboratory button samples. A computationally based homogenization heat treatment was applied to both alloys in order to eliminate segregation due to normal ingot solidification. The alloys fabricated well, with typical thermo-mechanical processing parameters being employed.

  13. A Note on Entropy Estimation.

    PubMed

    Schürmann, Thomas

    2015-10-01

    We compare an entropy estimator H(z) recently discussed by Zhang (2012) with two estimators, H(1) and H(2), introduced by Grassberger (2003) and Schürmann (2004). We prove the identity H(z) ≡ H(1), which has not been taken into account by Zhang (2012). Then we prove that the systematic error (bias) of H(1) is less than or equal to the bias of the ordinary likelihood (or plug-in) estimator of entropy. Finally, by numerical simulation, we verify that for the most interesting regime of small sample estimation and large event spaces, the estimator H(2) has a significantly smaller statistical error than H(z).

  14. Entropy shaping by shock decay

    NASA Astrophysics Data System (ADS)

    Piriz, A. R.; Sun, Y. B.; Tahir, N. A.

    2016-11-01

    A previous model [Piriz et al., Phys. Plasmas 23, 032704 (2016)] developed for describing the evolution of a shock wave driven by an arbitrary pressure pulse, is shown to be suitable for calculating the entropy shaping induced by a shock of decaying intensity. It is also shown that by allowing a causal connection between the shock and the piston, the model results to be complementary to the well-known self-similar solution for the impulsive loading problem, which is valid in the asymptotic regime when both fronts become decoupled. As a consequence, the entropy distribution depends on the details of the driving pressure pulse. A comparison with the available numerical simulations is presented.

  15. Preserved entropy and fragile magnetism

    DOE PAGES

    Canfield, Paul C.; Bud’ko, Sergey L.

    2016-07-05

    Here, a large swath of quantum critical and strongly correlated electron systems can be associated with the phenomena of preserved entropy and fragile magnetism. In this overview we present our thoughts and plans for the discovery and development of lanthanide and transition metal based, strongly correlated systems that are revealed by suppressed, fragile magnetism, quantum criticality, or grow out of preserved entropy. We will present and discuss current examples such as YbBiPt, YbAgGe, YbFe2Zn20, PrAg2In, BaFe2As2, CaFe2As2, LaCrSb3 and LaCrGe3 as part of our motivation and to provide illustrative examples.

  16. Preserved entropy and fragile magnetism.

    PubMed

    Canfield, Paul C; Bud'ko, Sergey L

    2016-08-01

    A large swath of quantum critical and strongly correlated electron systems can be associated with the phenomena of preserved entropy and fragile magnetism. In this overview we present our thoughts and plans for the discovery and development of lanthanide and transition metal based, strongly correlated systems that are revealed by suppressed, fragile magnetism, quantum criticality, or grow out of preserved entropy. We will present and discuss current examples such as YbBiPt, YbAgGe, YbFe2Zn20, PrAg2In, BaFe2As2, CaFe2As2, LaCrSb3 and LaCrGe3 as part of our motivation and to provide illustrative examples.

  17. Preserved entropy and fragile magnetism

    SciTech Connect

    Canfield, Paul C.; Bud’ko, Sergey L.

    2016-07-05

    Here, a large swath of quantum critical and strongly correlated electron systems can be associated with the phenomena of preserved entropy and fragile magnetism. In this overview we present our thoughts and plans for the discovery and development of lanthanide and transition metal based, strongly correlated systems that are revealed by suppressed, fragile magnetism, quantum criticality, or grow out of preserved entropy. We will present and discuss current examples such as YbBiPt, YbAgGe, YbFe2Zn20, PrAg2In, BaFe2As2, CaFe2As2, LaCrSb3 and LaCrGe3 as part of our motivation and to provide illustrative examples.

  18. Biological adaptabilities and quantum entropies.

    PubMed

    Kirby, Kevin G

    2002-01-01

    The entropy-based theory of adaptability set forth by Michael Conrad in the early 1970s continued to appear in his work for over two decades, and was the subject of the only book he published in his lifetime. He applied this theory to a host of subjects ranging from enzyme dynamics to sociology. This paper reviews the formalism of adaptability theory, clarifying some of its mathematical and interpretive difficulties. The theory frames the computational tradeoff principle, a thesis that was the most frequently recurring claim in his work. The formulation of adaptability theory presented here allows the introduction of quantum entropy functions into the theory, revealing an interesting relationship between adaptability and another one of Conrad's deep preoccupations, the role of quantum processes in life.

  19. Coverage-adjusted entropy estimation.

    PubMed

    Vu, Vincent Q; Yu, Bin; Kass, Robert E

    2007-09-20

    Data on 'neural coding' have frequently been analyzed using information-theoretic measures. These formulations involve the fundamental and generally difficult statistical problem of estimating entropy. We review briefly several methods that have been advanced to estimate entropy and highlight a method, the coverage-adjusted entropy estimator (CAE), due to Chao and Shen that appeared recently in the environmental statistics literature. This method begins with the elementary Horvitz-Thompson estimator, developed for sampling from a finite population, and adjusts for the potential new species that have not yet been observed in the sample-these become the new patterns or 'words' in a spike train that have not yet been observed. The adjustment is due to I. J. Good, and is called the Good-Turing coverage estimate. We provide a new empirical regularization derivation of the coverage-adjusted probability estimator, which shrinks the maximum likelihood estimate. We prove that the CAE is consistent and first-order optimal, with rate O(P)(1/log n), in the class of distributions with finite entropy variance and that, within the class of distributions with finite qth moment of the log-likelihood, the Good-Turing coverage estimate and the total probability of unobserved words converge at rate O(P)(1/(log n)(q)). We then provide a simulation study of the estimator with standard distributions and examples from neuronal data, where observations are dependent. The results show that, with a minor modification, the CAE performs much better than the MLE and is better than the best upper bound estimator, due to Paninski, when the number of possible words m is unknown or infinite.

  20. Steganography Detection Using Entropy Measures

    DTIC Science & Technology

    2012-11-16

    REPORT Steganography Detection Using Entropy MeasuresTechnical Report 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: Steganography is the science of...hiding the fact that some communication is taking place. In general encryption, encoding and decoding are not required to accomplish steganography ...However, encryption serves as a layer of protection when steganography fails. The first objective of steganography is hiding the existence of data exchange

  1. Entropy estimation and Fibonacci numbers

    NASA Astrophysics Data System (ADS)

    Timofeev, Evgeniy A.; Kaltchenko, Alexei

    2013-05-01

    We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. Notably, the number of distinct metric values for a set of sequences of length m is equal to Fm+3 - 1, where Fm is a Fibonacci number.

  2. NEGATIVE SYMPTOMS AND NEGATIVE SCHIZOPHRENIA

    PubMed Central

    Chaturvedi, S.K.; Gopinath, P.S.; Mathai, P. John; Michael, Albert

    1984-01-01

    SUMMARY This study determines the frequency distribution of prominent negative symptoms in a group of chronic, hospitalised schizophrenics. Thirty chronic Schizophrenic (D.S.M. III) patients were rated on the scale for Assessment of Negative Symptoms (SANS) and the prominent negative symptoms were correlated with age, sex and certain illness variables. Majority (80%) of patients had some or the other negative symptom, except thought blocking which was found in none. The subjective awareness of the symptoms was poor. Most negative symptoms were present to a severe degree in about 40% of cases. However, no significant correlation was found between severe negative symptoms and age or sex. Similarly, duration of illness, duration of hospitalisation or current medications did not influence negative symptoms to any appreciable degree. The implications are discussed. PMID:21965985

  3. Entropy estimation in Turing's perspective.

    PubMed

    Zhang, Zhiyi

    2012-05-01

    A new nonparametric estimator of Shannon's entropy on a countable alphabet is proposed and analyzed against the well-known plug-in estimator. The proposed estimator is developed based on Turing's formula, which recovers distributional characteristics on the subset of the alphabet not covered by a size-n sample. The fundamental switch in perspective brings about substantial gain in estimation accuracy for every distribution with finite entropy. In general, a uniform variance upper bound is established for the entire class of distributions with finite entropy that decays at a rate of O(ln(n)/n) compared to O([ln(n)]2/n) for the plug-in. In a wide range of subclasses, the variance of the proposed estimator converges at a rate of O(1/n), and this rate of convergence carries over to the convergence rates in mean squared errors in many subclasses. Specifically, for any finite alphabet, the proposed estimator has a bias decaying exponentially in n. Several new bias-adjusted estimators are also discussed.

  4. Linearity of holographic entanglement entropy

    NASA Astrophysics Data System (ADS)

    Almheiri, Ahmed; Dong, Xi; Swingle, Brian

    2017-02-01

    We consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of `entropy operators' in general systems with a large number of degrees of freedom.

  5. Entropy in an expanding universe.

    PubMed

    Frautschi, S

    1982-08-13

    The question of how the observed evolution of organized structures from initial chaos in the expanding universe can be reconciled with the laws of statistical mechanics is studied, with emphasis on effects of the expansion and gravity. Some major sources of entropy increase are listed. An expanding "causal" region is defined in which the entropy, though increasing, tends to fall further and further behind its maximum possible value, thus allowing for the development of order. The related questions of whether entropy will continue increasing without limit in the future, and whether such increase in the form of Hawking radiation or radiation from positronium might enable life to maintain itself permanently, are considered. Attempts to find a scheme for preserving life based on solid structures fail because events such as quantum tunneling recurrently disorganize matter on a very long but fixed time scale, whereas all energy sources slow down progressively in an expanding universe. However, there remains hope that other modes of life capable of maintaining themselves permanently can be found.

  6. Resting state fMRI entropy probes complexity of brain activity in adults with ADHD.

    PubMed

    Sokunbi, Moses O; Fung, Wilson; Sawlani, Vijay; Choppin, Sabine; Linden, David E J; Thome, Johannes

    2013-12-30

    In patients with attention deficit hyperactivity disorder (ADHD), quantitative neuroimaging techniques have revealed abnormalities in various brain regions, including the frontal cortex, striatum, cerebellum, and occipital cortex. Nonlinear signal processing techniques such as sample entropy have been used to probe the regularity of brain magnetoencephalography signals in patients with ADHD. In the present study, we extend this technique to analyse the complex output patterns of the 4 dimensional resting state functional magnetic resonance imaging signals in adult patients with ADHD. After adjusting for the effect of age, we found whole brain entropy differences (P=0.002) between groups and negative correlation (r=-0.45) between symptom scores and mean whole brain entropy values, indicating lower complexity in patients. In the regional analysis, patients showed reduced entropy in frontal and occipital regions bilaterally and a significant negative correlation between the symptom scores and the entropy maps at a family-wise error corrected cluster level of P<0.05 (P=0.001, initial threshold). Our findings support the hypothesis of abnormal frontal-striatal-cerebellar circuits in ADHD and the suggestion that sample entropy is a useful tool in revealing abnormalities in the brain dynamics of patients with psychiatric disorders.

  7. Formal groups and Z-entropies

    NASA Astrophysics Data System (ADS)

    Tempesta, Piergiulio

    2016-11-01

    We shall prove that the celebrated Rényi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Rényi. A crucial aspect is that every Z-entropy is composable (Tempesta 2016 Ann. Phys. 365, 180-197. (doi:10.1016/j.aop.2015.08.013)). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth Shannon-Khinchin axiom (postulating additivity), is a highly non-trivial requirement. Indeed, in the trace-form class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the non-trace form class, the Z-entropies arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying group-theoretical structure determines crucially the statistical properties of the corresponding entropies.

  8. Crowd macro state detection using entropy model

    NASA Astrophysics Data System (ADS)

    Zhao, Ying; Yuan, Mengqi; Su, Guofeng; Chen, Tao

    2015-08-01

    In the crowd security research area a primary concern is to identify the macro state of crowd behaviors to prevent disasters and to supervise the crowd behaviors. The entropy is used to describe the macro state of a self-organization system in physics. The entropy change indicates the system macro state change. This paper provides a method to construct crowd behavior microstates and the corresponded probability distribution using the individuals' velocity information (magnitude and direction). Then an entropy model was built up to describe the crowd behavior macro state. Simulation experiments and video detection experiments were conducted. It was verified that in the disordered state, the crowd behavior entropy is close to the theoretical maximum entropy; while in ordered state, the entropy is much lower than half of the theoretical maximum entropy. The crowd behavior macro state sudden change leads to the entropy change. The proposed entropy model is more applicable than the order parameter model in crowd behavior detection. By recognizing the entropy mutation, it is possible to detect the crowd behavior macro state automatically by utilizing cameras. Results will provide data support on crowd emergency prevention and on emergency manual intervention.

  9. Statistical mechanical theory of liquid entropy

    SciTech Connect

    Wallace, D.C.

    1993-07-01

    The multiparticle correlation expansion for the entropy of a classical monatomic liquid is presented. This entropy expresses the physical picture in which there is no free particle motion, but rather, each atom moves within a cage formed by its neighbors. The liquid expansion, including only pair correlations, gives an excellent account of the experimental entropy of most liquid metals, of liquid argon, and the hard sphere liquid. The pair correlation entropy is well approximated by a universal function of temperature. Higher order correlation entropy, due to n-particle irreducible correlations for n{ge}3, is significant in only a few liquid metals, and its occurrence suggests the presence of n-body forces. When the liquid theory is applied to the study of melting, the author discovers the important classification of normal and anomalous melting, according to whether there is not or is a significant change in the electronic structure upon melting, and he discovers the universal disordering entropy for melting of a monatomic crystal. Interesting directions for future research are: extension to include orientational correlations of molecules, theoretical calculation of the entropy of water, application to the entropy of the amorphous state, and correlational entropy of compressed argon. The author clarifies the relation among different entropy expansions in the recent literature.

  10. Formal groups and Z-entropies.

    PubMed

    Tempesta, Piergiulio

    2016-11-01

    We shall prove that the celebrated Rényi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Rényi. A crucial aspect is that every Z-entropy is composable (Tempesta 2016 Ann. Phys.365, 180-197. (doi:10.1016/j.aop.2015.08.013)). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth Shannon-Khinchin axiom (postulating additivity), is a highly non-trivial requirement. Indeed, in the trace-form class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the non-trace form class, the Z-entropies arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying group-theoretical structure determines crucially the statistical properties of the corresponding entropies.

  11. Combinatorial entropy and phase diagram of partially ordered ice phases.

    PubMed

    Macdowell, Luis G; Sanz, Eduardo; Vega, Carlos; Abascal, José Luis F

    2004-11-22

    A close analytical estimate for the combinatorial entropy of partially ordered ice phases is presented. The expression obtained is very general, as it can be used for any ice phase obeying the Bernal-Fowler rules. The only input required is a number of crystallographic parameters, and the experimentally observed proton site occupancies. For fully disordered phases such as hexagonal ice, it recovers the result deduced by Pauling, while for fully ordered ice it is found to vanish. Although the space groups determined for ice I, VI, and VII require random proton site occupancies, it is found that such random allocation of protons does not necessarily imply random orientational disorder. The theoretical estimate for the combinatorial entropy is employed together with free energy calculations in order to obtain the phase diagram of ice from 0 to 10 GPa. Overall qualitative agreement with experiment is found for the TIP4P model of water. An accurate estimate of the combinatorial entropy is found to play an important role in determining the stability of partially ordered ice phases, such as ice III and ice V.

  12. Entropy of adsorption of mixed surfactants from solutions onto the air/water interface

    USGS Publications Warehouse

    Chen, L.-W.; Chen, J.-H.; Zhou, N.-F.

    1995-01-01

    The partial molar entropy change for mixed surfactant molecules adsorbed from solution at the air/water interface has been investigated by surface thermodynamics based upon the experimental surface tension isotherms at various temperatures. Results for different surfactant mixtures of sodium dodecyl sulfate and sodium tetradecyl sulfate, decylpyridinium chloride and sodium alkylsulfonates have shown that the partial molar entropy changes for adsorption of the mixed surfactants were generally negative and decreased with increasing adsorption to a minimum near the maximum adsorption and then increased abruptly. The entropy decrease can be explained by the adsorption-orientation of surfactant molecules in the adsorbed monolayer and the abrupt entropy increase at the maximum adsorption is possible due to the strong repulsion between the adsorbed molecules.

  13. TASSRAP Input Module

    DTIC Science & Technology

    1977-07-29

    retrieve data necessary for the other modules to function. Initially there are 13 inputs, with the CRT dis - playing the information to be entered...id 46aý .0sso somma % 4bt--f. ft Aa W #4t - lQ *a - 4 c ,0 45 40 aK 43 ’ C = 04 ZSC 0 de *020.4 %- li’l ~ ~ ~ ~ ~ ~ & 1&.1 gol~ -,.-’ ow. -6 -N*4••1L...tv Z (𔃽 - C- ft %- ftb 0*4 *- -1 *4* (30 w ag &h 𔃾 0 a _6a .N I 0 A. 6.2 IL ILN ’ S MS 6C 0 to ~ 0 " di a S 0 m J *- -j f’ md op9 -9 $-. -6 = -A U .Af

  14. Local entropy of a nonequilibrium fermion system

    NASA Astrophysics Data System (ADS)

    Stafford, Charles A.; Shastry, Abhay

    2017-03-01

    The local entropy of a nonequilibrium system of independent fermions is investigated and analyzed in the context of the laws of thermodynamics. It is shown that the local temperature and chemical potential can only be expressed in terms of derivatives of the local entropy for linear deviations from local equilibrium. The first law of thermodynamics is shown to lead to an inequality, not equality, for the change in the local entropy as the nonequilibrium state of the system is changed. The maximum entropy principle (second law of thermodynamics) is proven: a nonequilibrium distribution has a local entropy less than or equal to a local equilibrium distribution satisfying the same constraints. It is shown that the local entropy of the system tends to zero when the local temperature tends to zero, consistent with the third law of thermodynamics.

  15. Corrected Entropy of BTZ Black Holes

    NASA Astrophysics Data System (ADS)

    Farahani, Hoda; Sadeghi, Jafar; Saadat, Hassan

    2012-12-01

    In this paper, corrected entropy of a class of BTZ black holes, include charge and rotation, studied. We obtain corrected Bekenstein-Hawking entropy and find that effect of charge viewed at order A -2, and effect of rotation viewed at order A -6, therefore Q and J don't have contribution in corrected entropy lower than the second order. We also write the first law of black hole thermodynamics for the case of charged rotating BTZ black hole.

  16. Monitoring Brain Injury With TSALLIS Entropy

    DTIC Science & Technology

    2001-10-25

    significant but still remains to be studied. Literature has pointed to the role of q in the entropy computation for EEG studies [10]. In our study it is... EEG in the form of reduction during the bad physiological function outcome. The reduction level and recovery rate of TE are also consistent with...USA Abstract- Nonextensive entropy measure, Tsallis Entropy (TE), was undertaken to monitor the brain injury after cardiac arrest. EEG of human and

  17. Entropy jump across an inviscid shock wave

    NASA Technical Reports Server (NTRS)

    Salas, Manuel D.; Iollo, Angelo

    1995-01-01

    The shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure are shown to be the same, however density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy, propagation equation cannot be used as a conservation law.

  18. Input Multiplicities in Process Control.

    ERIC Educational Resources Information Center

    Koppel, Lowell B.

    1983-01-01

    Describes research investigating potential effect of input multiplicity on multivariable chemical process control systems. Several simple processes are shown to exhibit the possibility of theoretical developments on input multiplicity and closely related phenomena are discussed. (JN)

  19. Modeling and generating input processes

    SciTech Connect

    Johnson, M.E.

    1987-01-01

    This tutorial paper provides information relevant to the selection and generation of stochastic inputs to simulation studies. The primary area considered is multivariate but much of the philosophy at least is relevant to univariate inputs as well. 14 refs.

  20. Mechanically Alloyed High Entropy Composite

    NASA Astrophysics Data System (ADS)

    Popescu, G.; Adrian, M. M.; Csaki, I.; Popescu, C. A.; Mitrică, D.; Vasile, S.; Carcea, I.

    2016-08-01

    In the last years high entropy alloys have been investigated due to their high hardness, high temperature stability and unusual properties that make these alloys to have significant interest. In comparison with traditional alloys that are based on two or three major elements, this new generation alloys consists at least of 5 principal elements, with the concentration between 5 and 35 at.%. The present paper reports synthesis of high entropy alloys (HEA) and high entropy composites (HEC) synthesized by mechanical alloying (MA). The equiatomic AlCrFeNiMn matrix was used for creating the HEA matrix, starting from elemental powders and as reinforcing material for composites was used pure graphite. The mechanical alloying process was carried out at different duration, in a high energy planetary ball mill, under argon atmosphere. The elemental powders alloying began after '5 hours of milling and was complete after 40 hours. The mechanical alloyed matrix and composite was pressed and heat treated under argon protection. The elemental powers were investigated for physical - technological properties, and by X-ray diffraction and scanning electron microscopy. Phase pressing operation was realized with a hydraulic press and the applied pressure was progressive. The sintering process was carried out at 850°C for 2 h. The X-ray diffraction revealed that the MA process resulted in solid solutions formation and also revealed body- centred cubic (BCC) and face-centred cubic (FCC) structures with average grain size around 40 nm. In addition, nanoscale particles were highlighted by scanning electron microscopy, as well as the homogeneity of the chemical composition of the matrix and composite that was confirmed by EDX microanalysis. It was noted that HEA matrix and HEA composites were processed with a high degree of compaction and with a quite large capacity of mixed powder densification (around 70%).

  1. Time dependence of Hawking radiation entropy

    SciTech Connect

    Page, Don N.

    2013-09-01

    If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4πM{sub 0}{sup 2}, or about 7.509M{sub 0}{sup 2} ≈ 6.268 × 10{sup 76}(M{sub 0}/M{sub s}un){sup 2}, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018M{sub 0}{sup 2} ≈ 1.254 × 10{sup 77}(M{sub 0}/M{sub s}un){sup 2}, and then decreases back down to 4πM{sub 0}{sup 2} = 1.049 × 10{sup 77}(M{sub 0}/M{sub s}un){sup 2}.

  2. Time dependence of Hawking radiation entropy

    NASA Astrophysics Data System (ADS)

    Page, Don N.

    2013-09-01

    If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4πM02, or about 7.509M02 ≈ 6.268 × 1076(M0/Msolar)2, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018M02 ≈ 1.254 × 1077(M0/Msolar)2, and then decreases back down to 4πM02 = 1.049 × 1077(M0/Msolar)2.

  3. Physical entropy and the senses.

    PubMed

    Norwich, Kenneth H

    2005-01-01

    With reference to two specific modalities of sensation, the taste of saltiness of chloride salts, and the loudness of steady tones, it is shown that the laws of sensation (logarithmic and power laws) are expressions of the entropy per mole of the stimulus. That is, the laws of sensation are linear functions of molar entropy. In partial verification of this hypothesis, we are able to derive an approximate value for the gas constant, a fundamental physical constant, directly from psychophysical measurements. The significance of our observation lies in the linking of the phenomenon of "sensation" directly to a physical measure. It suggests that if the laws of physics are universal, the laws of sensation and perception are similarly universal. It also connects the sensation of a simple, steady physical signal with the molecular structure of the signal: the greater the number of microstates or complexions of the stimulus signal, the greater the magnitude of the sensation (saltiness or loudness). The hypothesis is currently tested on two sensory modalities.

  4. The Kepler Input Catalog

    NASA Astrophysics Data System (ADS)

    Latham, D. W.; Brown, T. M.; Monet, D. G.; Everett, M.; Esquerdo, G. A.; Hergenrother, C. W.

    2005-12-01

    The Kepler mission will monitor 170,000 planet-search targets during the first year, and 100,000 after that. The Kepler Input Catalog (KIC) will be used to select optimum targets for the search for habitable earth-like transiting planets. The KIC will include all known catalogued stars in an area of about 177 square degrees centered at RA 19:22:40 and Dec +44:30 (l=76.3 and b=+13.5). 2MASS photometry will be supplemented with new ground-based photometry obtained in the SDSS g, r, i, and z bands plus a custom filter centered on the Mg b lines, using KeplerCam on the 48-inch telescope at the Whipple Observatory on Mount Hopkins, Arizona. The photometry will be used to estimate stellar characteristics for all stars brighter than K 14.5 mag. The KIC will include effective temperature, surface gravity, metallicity, reddening, distance, and radius estimates for these stars. The CCD images are pipeline processed to produce instrumental magnitudes at PSI. The photometry is then archived and transformed to the SDSS system at HAO, where the astrophysical analysis of the stellar characteristics is carried out. The results are then merged with catalogued data at the USNOFS to produce the KIC. High dispersion spectroscopy with Hectochelle on the MMT will be used to supplement the information for many of the most interesting targets. The KIC will be released before launch for use by the astronomical community and will be available for queries over the internet. Support from the Kepler mission is gratefully acknowledged.

  5. Cross approximate entropy analysis of nocturnal oximetry signals in the diagnosis of the obstructive sleep apnea syndrome.

    PubMed

    Alvarez, Daniel; Hornero, Roberto; Garcia, Mariá; del Campo, Felix; Zamarron, Carlos; López, Miguel

    2006-01-01

    This study is focused on the analysis of blood oxygen saturation (SaO(2)) and heart rate (HR) from nocturnal oximetry using cross approximate entropy (Cross-ApEn). We assessed its usefulness in screening obstructive sleep apnea (OSA) syndrome. We applied Cross-ApEn(m,r,N) to quantify the asynchrony between paired SaO(2) and HR records of 74 patients (44 with a positive OSA diagnosis and 30 with a negative OSA diagnosis). Cross-ApEn values were significantly lower in the OSA positive group compared with those obtained in the OSA negative group. A receiver operating characteristic (ROC) analysis showed that the best results, in terms of diagnostic accuracy, were achieved with m = 2 and r = 0.6. With these input parameters, the optimum decision threshold was found at 1.7, where we achieved 95.5% sensitivity, 73.3% specificity and 86.5% accuracy. Further analyses should be carried out with new and larger data sets to test the usefulness of our methodology prospectively.

  6. Entropy and generalized least square methods in assessment of the regional value of streamgages

    USGS Publications Warehouse

    Markus, M.; Vernon, Knapp H.; Tasker, Gary D.

    2003-01-01

    The Illinois State Water Survey performed a study to assess the streamgaging network in the State of Illinois. One of the important aspects of the study was to assess the regional value of each station through an assessment of the information transfer among gaging records for low, average, and high flow conditions. This analysis was performed for the main hydrologic regions in the State, and the stations were initially evaluated using a new approach based on entropy analysis. To determine the regional value of each station within a region, several information parameters, including total net information, were defined based on entropy. Stations were ranked based on the total net information. For comparison, the regional value of the same stations was assessed using the generalized least square regression (GLS) method, developed by the US Geological Survey. Finally, a hybrid combination of GLS and entropy was created by including a function of the negative net information as a penalty function in the GLS. The weights of the combined model were determined to maximize the average correlation with the results of GLS and entropy. The entropy and GLS methods were evaluated using the high-flow data from southern Illinois stations. The combined method was compared with the entropy and GLS approaches using the high-flow data from eastern Illinois stations. ?? 2003 Elsevier B.V. All rights reserved.

  7. Entropy Generation in a Chemical Reaction

    ERIC Educational Resources Information Center

    Miranda, E. N.

    2010-01-01

    Entropy generation in a chemical reaction is analysed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic equation of an elementary first-order reaction is used to show that entropy production is always positive. A…

  8. The Origins of the Entropy Concept

    NASA Astrophysics Data System (ADS)

    Darrigol, Olivier

    To this day entropy remains a strange, difficult, and multiform concept. Even the great Henri Poincaré renounced precisely defining energy and entropy. In order to justify the success of the two laws of thermodynamics for his students at the Sorbonne, he turned to history:

  9. Entropy estimation of very short symbolic sequences

    NASA Astrophysics Data System (ADS)

    Lesne, Annick; Blanc, Jean-Luc; Pezard, Laurent

    2009-04-01

    While entropy per unit time is a meaningful index to quantify the dynamic features of experimental time series, its estimation is often hampered in practice by the finite length of the data. We here investigate the performance of entropy estimation procedures, relying either on block entropies or Lempel-Ziv complexity, when only very short symbolic sequences are available. Heuristic analytical arguments point at the influence of temporal correlations on the bias and statistical fluctuations, and put forward a reduced effective sequence length suitable for error estimation. Numerical studies are conducted using, as benchmarks, the wealth of different dynamic regimes generated by the family of logistic maps and stochastic evolutions generated by a Markov chain of tunable correlation time. Practical guidelines and validity criteria are proposed. For instance, block entropy leads to a dramatic overestimation for sequences of low entropy, whereas it outperforms Lempel-Ziv complexity at high entropy. As a general result, the quality of entropy estimation is sensitive to the sequence temporal correlation hence self-consistently depends on the entropy value itself, thus promoting a two-step procedure. Lempel-Ziv complexity is to be preferred in the first step and remains the best estimator for highly correlated sequences.

  10. Entropy estimation of very short symbolic sequences.

    PubMed

    Lesne, Annick; Blanc, Jean-Luc; Pezard, Laurent

    2009-04-01

    While entropy per unit time is a meaningful index to quantify the dynamic features of experimental time series, its estimation is often hampered in practice by the finite length of the data. We here investigate the performance of entropy estimation procedures, relying either on block entropies or Lempel-Ziv complexity, when only very short symbolic sequences are available. Heuristic analytical arguments point at the influence of temporal correlations on the bias and statistical fluctuations, and put forward a reduced effective sequence length suitable for error estimation. Numerical studies are conducted using, as benchmarks, the wealth of different dynamic regimes generated by the family of logistic maps and stochastic evolutions generated by a Markov chain of tunable correlation time. Practical guidelines and validity criteria are proposed. For instance, block entropy leads to a dramatic overestimation for sequences of low entropy, whereas it outperforms Lempel-Ziv complexity at high entropy. As a general result, the quality of entropy estimation is sensitive to the sequence temporal correlation hence self-consistently depends on the entropy value itself, thus promoting a two-step procedure. Lempel-Ziv complexity is to be preferred in the first step and remains the best estimator for highly correlated sequences.

  11. Rudolf Clausius and the road to entropy

    NASA Astrophysics Data System (ADS)

    Cropper, William H.

    1986-12-01

    That Rudolf Clausius invented the entropy concept is well known, but less familiar is the argument that served as his inspiration. This paper traces the development of Clausius' ``transformation theory'' of heat, which finally persuaded him to define the measure of transformation equivalence he called entropy.

  12. Generalized Entropic Uncertainty Relations with Tsallis' Entropy

    NASA Technical Reports Server (NTRS)

    Portesi, M.; Plastino, A.

    1996-01-01

    A generalization of the entropic formulation of the Uncertainty Principle of Quantum Mechanics is considered with the introduction of the q-entropies recently proposed by Tsallis. The concomitant generalized measure is illustrated for the case of phase and number operators in quantum optics. Interesting results are obtained when making use of q-entropies as the basis for constructing generalized entropic uncertainty measures.

  13. Ehrenfest's Lottery--Time and Entropy Maximization

    ERIC Educational Resources Information Center

    Ashbaugh, Henry S.

    2010-01-01

    Successful teaching of the Second Law of Thermodynamics suffers from limited simple examples linking equilibrium to entropy maximization. I describe a thought experiment connecting entropy to a lottery that mixes marbles amongst a collection of urns. This mixing obeys diffusion-like dynamics. Equilibrium is achieved when the marble distribution is…

  14. Entropy and Certainty in Lossless Data Compression

    ERIC Educational Resources Information Center

    Jacobs, James Jay

    2009-01-01

    Data compression is the art of using encoding techniques to represent data symbols using less storage space compared to the original data representation. The encoding process builds a relationship between the entropy of the data and the certainty of the system. The theoretical limits of this relationship are defined by the theory of entropy in…

  15. Campbell's Rule for Estimating Entropy Changes

    ERIC Educational Resources Information Center

    Jensen, William B.

    2004-01-01

    Campbell's rule for estimating entropy changes is discussed in relation to an earlier article by Norman Craig, where it was proposed that the approximate value of the entropy of reaction was related to net moles of gas consumed or generated. It was seen that the average for Campbell's data set was lower than that for Craig's data set and…

  16. Chemical Engineering Students' Ideas of Entropy

    ERIC Educational Resources Information Center

    Haglund, Jesper; Andersson, Staffan; Elmgren, Maja

    2015-01-01

    Thermodynamics, and in particular entropy, has been found to be challenging for students, not least due to its abstract character. Comparisons with more familiar and concrete domains, by means of analogy and metaphor, are commonly used in thermodynamics teaching, in particular the metaphor "entropy is disorder." However, this particular…

  17. Progress in High-Entropy Alloys

    SciTech Connect

    Gao, Michael C

    2013-12-01

    Strictly speaking, high-entropy alloys (HEAs) refer to single-phase, solid-solution alloys with multiprincipal elements in an equal or a near-equal molar ratio whose configurational entropy is tremendously high. This special topic was organized to reflect the focus and diversity of HEA research topics in the community.

  18. Low Streamflow Forcasting using Minimum Relative Entropy

    NASA Astrophysics Data System (ADS)

    Cui, H.; Singh, V. P.

    2013-12-01

    Minimum relative entropy spectral analysis is derived in this study, and applied to forecast streamflow time series. Proposed method extends the autocorrelation in the manner that the relative entropy of underlying process is minimized so that time series data can be forecasted. Different prior estimation, such as uniform, exponential and Gaussian assumption, is taken to estimate the spectral density depending on the autocorrelation structure. Seasonal and nonseasonal low streamflow series obtained from Colorado River (Texas) under draught condition is successfully forecasted using proposed method. Minimum relative entropy determines spectral of low streamflow series with higher resolution than conventional method. Forecasted streamflow is compared to the prediction using Burg's maximum entropy spectral analysis (MESA) and Configurational entropy. The advantage and disadvantage of each method in forecasting low streamflow is discussed.

  19. Trends of stellar entropy along stellar evolution

    NASA Astrophysics Data System (ADS)

    de Avellar, Guilherme Bronzato, Marcio; Alvares de Souza, Rodrigo; Horvath, Jorge Ernesto

    2016-02-01

    This paper is devoted to discussing the difference in the thermodynamic entropy budget per baryon in each type of stellar object found in the Universe. We track and discuss the actual decrease of the stored baryonic thermodynamic entropy from the most primitive molecular cloud up to the final fate of matter in black holes, passing through evolved states of matter as found in white dwarfs and neutron stars. We then discuss the case of actual stars with different masses throughout their evolution, clarifying the role of the virial equilibrium condition for the decrease in entropy and related issues. Finally, we discuss the role of gravity in driving the composition and the structural changes of stars with different Main Sequence masses during their evolution up to the final product. Particularly, we discuss the entropy of a black hole in this context arguing that the dramatic increase in its entropy, differently from the other cases, is due to the gravitational field itself.

  20. The role of entropy in magnetotail dynamics

    SciTech Connect

    Birn, Joachim; Zaharia, Sorin; Hesse, Michael

    2008-01-01

    The role of entropy conservation and loss in magnetospheric dynamics, particularly in relation to substorm phases, is discussed on the basis of MHD theory and simulations, using comparisons with PIC simulations for validation. Entropy conservation appears to be a crucial element leading to the formation of thin embedded current sheets in the late substorm growth phase and the potential loss of equilibrium. Entropy loss (in the form of plasmoids) is essential in the earthward transport of flux tubes (bubbles, bursty bulk flows). Entropy loss also changes the tail stability properties and may render ballooning modes unstable and thus contribute to cross-tail variability. We illustrate these effects through results from theory and simulations. Entropy conservation also governs the accessibility of final states of evolution and the amount of energy that may be released.

  1. Entanglement entropy in top-down models

    NASA Astrophysics Data System (ADS)

    Jones, Peter A. R.; Taylor, Marika

    2016-08-01

    We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entan-glement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduc-tion over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.

  2. Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies

    NASA Astrophysics Data System (ADS)

    Weilenmann, Mirjam; Kraemer, Lea; Faist, Philippe; Renner, Renato

    2016-12-01

    Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [E. H. Lieb and J. Yngvason Proc. R. Soc. 469, 20130408 (2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalization to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in nonequilibrium thermodynamics correspond to entropies used in one-shot information theory.

  3. Entanglement entropy of non-unitary conformal field theory

    NASA Astrophysics Data System (ADS)

    Bianchini, D.; Castro-Alvaredo, O.; Doyon, B.; Levi, E.; Ravanini, F.

    2015-01-01

    Here we show that the Rényi entanglement entropy of a region of large size ℓ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as {{S}n}˜ \\frac{{{c}eff}(n+1)}{6n}log \\ell , where {{c}eff}=c-24Δ \\gt 0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and Δ \

  4. Serial Input Output

    SciTech Connect

    Waite, Anthony; /SLAC

    2011-09-07

    Serial Input/Output (SIO) is designed to be a long term storage format of a sophistication somewhere between simple ASCII files and the techniques provided by inter alia Objectivity and Root. The former tend to be low density, information lossy (floating point numbers lose precision) and inflexible. The latter require abstract descriptions of the data with all that that implies in terms of extra complexity. The basic building blocks of SIO are streams, records and blocks. Streams provide the connections between the program and files. The user can define an arbitrary list of streams as required. A given stream must be opened for either reading or writing. SIO does not support read/write streams. If a stream is closed during the execution of a program, it can be reopened in either read or write mode to the same or a different file. Records represent a coherent grouping of data. Records consist of a collection of blocks (see next paragraph). The user can define a variety of records (headers, events, error logs, etc.) and request that any of them be written to any stream. When SIO reads a file, it first decodes the record name and if that record has been defined and unpacking has been requested for it, SIO proceeds to unpack the blocks. Blocks are user provided objects which do the real work of reading/writing the data. The user is responsible for writing the code for these blocks and for identifying these blocks to SIO at run time. To write a collection of blocks, the user must first connect them to a record. The record can then be written to a stream as described above. Note that the same block can be connected to many different records. When SIO reads a record, it scans through the blocks written and calls the corresponding block object (if it has been defined) to decode it. Undefined blocks are skipped. Each of these categories (streams, records and blocks) have some characteristics in common. Every stream, record and block has a name with the condition that each

  5. Channel capacity and receiver deployment optimization for multi-input multi-output visible light communications.

    PubMed

    Wang, Jin-Yuan; Dai, Jianxin; Guan, Rui; Jia, Linqiong; Wang, Yongjin; Chen, Ming

    2016-06-13

    Multi-input multi-output (MIMO) technique is attractive for visible light communication (VLC), which exploits the high signal-to-noise ratio (SNR) of a single channel to overcome the capacity limitation due to the small modulation bandwidth of the light emitting diode. This paper establishes a MIMO VLC system under the non-negativity, peak power and dimmable average power constraints. Assume that perfect channel state information at the transmitter is known, the MIMO channel is changed to parallel, non-interfering sub-channels by using the singular value decomposition (SVD). Based on the SVD, the lower bound on the channel capacity for MIMO VLC is derived by employing entropy power inequality and variational method. Moreover, by maximizing the derived lower bound on the capacity under the given constraints, the receiver deployment optimization problem is formulated. The problem is solved by employing the principle of particle swarm optimization. Numerical results verify the derived capacity bound and the proposed deployment optimization scheme.

  6. SDR Input Power Estimation Algorithms

    NASA Technical Reports Server (NTRS)

    Nappier, Jennifer M.; Briones, Janette C.

    2013-01-01

    The General Dynamics (GD) S-Band software defined radio (SDR) in the Space Communications and Navigation (SCAN) Testbed on the International Space Station (ISS) provides experimenters an opportunity to develop and demonstrate experimental waveforms in space. The SDR has an analog and a digital automatic gain control (AGC) and the response of the AGCs to changes in SDR input power and temperature was characterized prior to the launch and installation of the SCAN Testbed on the ISS. The AGCs were used to estimate the SDR input power and SNR of the received signal and the characterization results showed a nonlinear response to SDR input power and temperature. In order to estimate the SDR input from the AGCs, three algorithms were developed and implemented on the ground software of the SCAN Testbed. The algorithms include a linear straight line estimator, which used the digital AGC and the temperature to estimate the SDR input power over a narrower section of the SDR input power range. There is a linear adaptive filter algorithm that uses both AGCs and the temperature to estimate the SDR input power over a wide input power range. Finally, an algorithm that uses neural networks was designed to estimate the input power over a wide range. This paper describes the algorithms in detail and their associated performance in estimating the SDR input power.

  7. Entropy of uremia and dialysis technology.

    PubMed

    Ronco, Claudio

    2013-01-01

    The second law of thermodynamics applies with local exceptions to patient history and therapy interventions. Living things preserve their low level of entropy throughout time because they receive energy from their surroundings in the form of food. They gain their order at the expense of disordering the nutrients they consume. Death is the thermodynamically favored state: it represents a large increase in entropy as molecular structure yields to chaos. The kidney is an organ dissipating large amounts of energy to maintain the level of entropy of the organism as low as possible. Diseases, and in particular uremia, represent conditions of rapid increase in entropy. Therapeutic strategies are oriented towards a reduction in entropy or at least a decrease in the speed of entropy increase. Uremia is a process accelerating the trend towards randomness and disorder (increase in entropy). Dialysis is a factor external to the patient that tends to reduce the level of entropy caused by kidney disease. Since entropy can only increase in closed systems, energy and work must be spent to limit the entropy of uremia. This energy should be adapted to the system (patient) and be specifically oriented and personalized. This includes a multidimensional effort to achieve an adequate dialysis that goes beyond small molecular weight solute clearance. It includes a biological plan for recovery of homeostasis and a strategy towards long-term rehabilitation of the patient. Such objectives can be achieved with a combination of technology and innovation to answer specific questions that are still present after 60 years of dialysis history. This change in the individual bioentropy may represent a local exception to natural trends as the patient could be considered an isolated universe responding to the classic laws of thermodynamics.

  8. Negative Certainty

    ERIC Educational Resources Information Center

    Ariso, José María

    2017-01-01

    The definitions of "negative knowledge" and the studies in this regard published to date have not considered the categorial distinction Wittgenstein established between knowledge and certainty. Hence, the important role that certainty, despite its omission, should have in these definitions and studies has not yet been shown. In this…

  9. Negative Numbers

    ERIC Educational Resources Information Center

    Galbraith, Mary J.

    1974-01-01

    Examination of models for representing integers demonstrates that formal operational thought is required for establishing the operations on integers. Advocated is the use of many models for introducing negative numbers but, apart from addition, it is recommended that operations on integers be delayed until the formal operations stage. (JP)

  10. Controlling chaos in balanced neural circuits with input spike trains

    NASA Astrophysics Data System (ADS)

    Engelken, Rainer; Wolf, Fred

    The cerebral cortex can be seen as a system of neural circuits driving each other with spike trains. Here we study how the statistics of these spike trains affects chaos in balanced target circuits.Earlier studies of chaos in balanced neural circuits either used a fixed input [van Vreeswijk, Sompolinsky 1996, Monteforte, Wolf 2010] or white noise [Lajoie et al. 2014]. We study dynamical stability of balanced networks driven by input spike trains with variable statistics. The analytically obtained Jacobian enables us to calculate the complete Lyapunov spectrum. We solved the dynamics in event-based simulations and calculated Lyapunov spectra, entropy production rate and attractor dimension. We vary correlations, irregularity, coupling strength and spike rate of the input and action potential onset rapidness of recurrent neurons.We generally find a suppression of chaos by input spike trains. This is strengthened by bursty and correlated input spike trains and increased action potential onset rapidness. We find a link between response reliability and the Lyapunov spectrum. Our study extends findings in chaotic rate models [Molgedey et al. 1992] to spiking neuron models and opens a novel avenue to study the role of projections in shaping the dynamics of large neural circuits.

  11. Entropy Splitting and Numerical Dissipation

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Vinokur, M.; Djomehri, M. J.

    1999-01-01

    A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock

  12. Area terms in entanglement entropy

    NASA Astrophysics Data System (ADS)

    Casini, Horacio; Mazzitelli, F. D.; Testé, Eduardo

    2015-05-01

    We discuss area terms in entanglement entropy and show that a recent formula by Rosenhaus and Smolkin is equivalent to the term involving a correlator of traces of the stress tensor in the Adler-Zee formula for the renormalization of the Newton constant. We elaborate on how to fix the ambiguities in these formulas: Improving terms for the stress tensor of free fields, boundary terms in the modular Hamiltonian, and contact terms in the Euclidean correlation functions. We make computations for free fields and show how to apply these calculations to understand some results for interacting theories which have been studied in the literature. We also discuss an application to the F-theorem.

  13. Increasing entropy for colloidal stabilization

    PubMed Central

    Mo, Songping; Shao, Xuefeng; Chen, Ying; Cheng, Zhengdong

    2016-01-01

    Stability is of paramount importance in colloidal applications. Attraction between colloidal particles is believed to lead to particle aggregation and phase separation; hence, stability improvement can be achieved through either increasing repulsion or reducing attraction by modifying the fluid medium or by using additives. Two traditional mechanisms for colloidal stability are electrostatic stabilization and steric stabilization. However, stability improvement by mixing attractive and unstable particles has rarely been considered. Here, we emphasize the function of mixing entropy in colloidal stabilization. Dispersion stability improvement is demonstrated by mixing suspensions of attractive nanosized titania spheres and platelets. A three-dimensional phase diagram is proposed to illustrate the collaborative effects of particle mixing and particle attraction on colloidal stability. This discovery provides a novel method for enhancing colloidal stability and opens a novel opportunity for engineering applications. PMID:27872473

  14. Urban Transfer Entropy across Scales

    PubMed Central

    Murcio, Roberto

    2015-01-01

    The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Urban migration to and from cities is characterised as non-random and following non-random pathways. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity between scales is important in determining how the interplay of local/regional urban policies may affect the distribution of urban settlements. In order to quantify these relationships, we follow an information theoretic approach using the concept of Transfer Entropy. Our analysis is based on a stochastic urban fractal model, which mimics urban growing settlements and migration waves. The results indicate how different policies could affect urban morphology in terms of the information generated across geographical scales. PMID:26207628

  15. Entropy concepts in classical electrodynamics

    NASA Astrophysics Data System (ADS)

    Cole, Daniel C.

    2002-11-01

    Aspects of entropy and related thermodynamic analyses are discussed here that have been deduced in recent years in the area of classical electrodynamics. A motivating factor for most of this work has been an attempted theory of nature often called, "stochastic electrodynamics" (SED). This theory involves classical electrodynamics (Maxwell's equations plus the relativistic version of Newton's second law of motion for particles), but with the consideration that motion and fluctuations should not necessarily be assumed to reduce to zero at temperature T = 0. Both fairly subtle and rather blatant assumptions were often imposed in early thermodynamic analyses of electrodynamic systems that prevented the analyses from being sufficiently general to account for these "zero-point" properties, which hindered classical physics from being able to better account for quantum mechanical phenomena observed in nature. In turn, such thermodynamic considerations have helped motivate many of the key ideas of SED.

  16. Increasing entropy for colloidal stabilization

    NASA Astrophysics Data System (ADS)

    Mo, Songping; Shao, Xuefeng; Chen, Ying; Cheng, Zhengdong

    2016-11-01

    Stability is of paramount importance in colloidal applications. Attraction between colloidal particles is believed to lead to particle aggregation and phase separation; hence, stability improvement can be achieved through either increasing repulsion or reducing attraction by modifying the fluid medium or by using additives. Two traditional mechanisms for colloidal stability are electrostatic stabilization and steric stabilization. However, stability improvement by mixing attractive and unstable particles has rarely been considered. Here, we emphasize the function of mixing entropy in colloidal stabilization. Dispersion stability improvement is demonstrated by mixing suspensions of attractive nanosized titania spheres and platelets. A three-dimensional phase diagram is proposed to illustrate the collaborative effects of particle mixing and particle attraction on colloidal stability. This discovery provides a novel method for enhancing colloidal stability and opens a novel opportunity for engineering applications.

  17. Consistent thermostatistics forbids negative absolute temperatures

    NASA Astrophysics Data System (ADS)

    Dunkel, Jörn; Hilbert, Stefan

    2014-01-01

    Over the past 60 years, a considerable number of theories and experiments have claimed the existence of negative absolute temperature in spin systems and ultracold quantum gases. This has led to speculation that ultracold gases may be dark-energy analogues and also suggests the feasibility of heat engines with efficiencies larger than one. Here, we prove that all previous negative temperature claims and their implications are invalid as they arise from the use of an entropy definition that is inconsistent both mathematically and thermodynamically. We show that the underlying conceptual deficiencies can be overcome if one adopts a microcanonical entropy functional originally derived by Gibbs. The resulting thermodynamic framework is self-consistent and implies that absolute temperature remains positive even for systems with a bounded spectrum. In addition, we propose a minimal quantum thermometer that can be implemented with available experimental techniques.

  18. How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems.

    PubMed

    Hanel, Rudolf; Thurner, Stefan; Gell-Mann, Murray

    2014-05-13

    The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process.

  19. How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems

    PubMed Central

    Hanel, Rudolf; Thurner, Stefan; Gell-Mann, Murray

    2014-01-01

    The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann–Gibbs–Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon–Khinchin axioms, the -entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process. PMID:24782541

  20. On entropy, financial markets and minority games

    NASA Astrophysics Data System (ADS)

    Zapart, Christopher A.

    2009-04-01

    The paper builds upon an earlier statistical analysis of financial time series with Shannon information entropy, published in [L. Molgedey, W. Ebeling, Local order, entropy and predictability of financial time series, European Physical Journal B-Condensed Matter and Complex Systems 15/4 (2000) 733-737]. A novel generic procedure is proposed for making multistep-ahead predictions of time series by building a statistical model of entropy. The approach is first demonstrated on the chaotic Mackey-Glass time series and later applied to Japanese Yen/US dollar intraday currency data. The paper also reinterprets Minority Games [E. Moro, The minority game: An introductory guide, Advances in Condensed Matter and Statistical Physics (2004)] within the context of physical entropy, and uses models derived from minority game theory as a tool for measuring the entropy of a model in response to time series. This entropy conditional upon a model is subsequently used in place of information-theoretic entropy in the proposed multistep prediction algorithm.

  1. Negative specific heat of a magnetically self-confined plasma torus

    PubMed Central

    Kiessling, Michael K.-H.; Neukirch, Thomas

    2003-01-01

    It is shown that the thermodynamic maximum-entropy principle predicts negative specific heat for a stationary, magnetically self-confined current-carrying plasma torus. Implications for the magnetic self-confinement of fusion plasma are considered. PMID:12576553

  2. Growth rate, population entropy, and perturbation theory.

    PubMed

    Demetrius, L

    1989-04-01

    This paper is concerned with the connection between two classes of population variables: measures of population growth rate--the Malthusian parameter, the net reproduction rate, the gross reproduction rate, and the mean life expectancy; and measures of demographic heterogeneity--population entropy. It is shown that the entropy functions predict the response of the growth rate parameters to perturbations in the age-specific fecundity and mortality schedule. These results are invoked to introduce the notion of environmental intensity. The intensity function, expressed in terms of the entropy parameters, is applied to give a comparative study of the effect of environmental factors on the dynamics of Swedish and French populations.

  3. Boundary fluctuations and a reduction entropy

    NASA Astrophysics Data System (ADS)

    Herzog, Christopher; Huang, Kuo-Wei

    2017-01-01

    The boundary Weyl anomalies live on a codimension-1 boundary, ∂M . The entanglement entropy originates from infinite correlations on both sides of a codimension-2 surface, Σ . Motivated to have a further understanding of the boundary effects, we introduce a notion of reduction entropy, which, guided by thermodynamics, is a combination of the boundary effective action and the boundary stress tensor defined by allowing the metric on ∂M to fluctuate. We discuss how a reduction might be performed so that the reduction entropy reproduces the entanglement structure.

  4. A psychophysical theory of Shannon entropy.

    PubMed

    Takahashi, Taiki

    2013-01-01

    Connections between information theory and decision under uncertainty have been attracting attention in econophysics, neuroeconomics and quantum decision theory. This paper proposes a psychophysical theory of Shannon entropy based on a mathematical equivalence of delay and uncertainty in decision-making, and psychophysics of the perception of waiting time in probabilistic choices. Furthermore, it is shown that the well-known Shannon entropy is a special case of the general psychophysical entropy. Future directions in the application of the present theory to studies in econophysics and neuroeconomics are discussed.

  5. REL - English Bulk Data Input.

    ERIC Educational Resources Information Center

    Bigelow, Richard Henry

    A bulk data input processor which is available for the Rapidly Extensible Language (REL) English versions is described. In REL English versions, statements that declare names of data items and their interrelationships normally are lines from a terminal or cards in a batch input stream. These statements provide a convenient means of declaring some…

  6. Inputs for L2 Acquisition.

    ERIC Educational Resources Information Center

    Saleemi, Anjum P.

    1989-01-01

    Major approaches of describing or examining linguistic data from a potential target language (input) are analyzed for adequacy in addressing the concerns of second language learning theory. Suggestions are made for making the best of these varied concepts of input and for reformulation of a unified concept. (MSE)

  7. Input in Second Language Acquisition.

    ERIC Educational Resources Information Center

    Gass, Susan M., Ed.; Madden, Carolyn G., Ed.

    This collection of conference papers includes: "When Does Teacher Talk Work as Input?"; "Cultural Input in Second Language Learning"; "Skilled Variation in a Kindergarten Teacher's Use of Foreigner Talk"; "Teacher-Pupil Interaction in Second Language Development"; "Foreigner Talk in the University…

  8. Structured chaos shapes spike-response noise entropy in balanced neural networks.

    PubMed

    Lajoie, Guillaume; Thivierge, Jean-Philippe; Shea-Brown, Eric

    2014-01-01

    Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. For many models of these networks, a striking feature is that their dynamics are chaotic and thus, are sensitive to small perturbations. How does this chaos manifest in the neural code? Specifically, how variable are the spike patterns that such a network produces in response to an input signal? To answer this, we derive a bound for a general measure of variability-spike-train entropy. This leads to important insights on the variability of multi-cell spike pattern distributions in large recurrent networks of spiking neurons responding to fluctuating inputs. The analysis is based on results from random dynamical systems theory and is complemented by detailed numerical simulations. We find that the spike pattern entropy is an order of magnitude lower than what would be extrapolated from single cells. This holds despite the fact that network coupling becomes vanishingly sparse as network size grows-a phenomenon that depends on "extensive chaos," as previously discovered for balanced networks without stimulus drive. Moreover, we show how spike pattern entropy is controlled by temporal features of the inputs. Our findings provide insight into how neural networks may encode stimuli in the presence of inherently chaotic dynamics.

  9. Black hole entropy, topological entropy and the Baum-Connes conjecture in K-theory

    NASA Astrophysics Data System (ADS)

    Zois, Ioannis P.

    2002-03-01

    We shall try to show a relation between black hole (BH) entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for BHs, provided by superstring theory, in the more general noncommutative geometric context of M-theory following the approach of Connes-Douglas-Schwarz.

  10. Modified correlation entropy estimation for a noisy chaotic time series.

    PubMed

    Jayawardena, A W; Xu, Pengcheng; Li, W K

    2010-06-01

    A method of estimating the Kolmogorov-Sinai (KS) entropy, herein referred to as the modified correlation entropy, is presented. The method can be applied to both noise-free and noisy chaotic time series. It has been applied to some clean and noisy data sets and the numerical results show that the modified correlation entropy is closer to the KS entropy of the nonlinear system calculated by the Lyapunov spectrum than the general correlation entropy. Moreover, the modified correlation entropy is more robust to noise than the correlation entropy.

  11. Stimulus-dependent Maximum Entropy Models of Neural Population Codes

    PubMed Central

    Segev, Ronen; Schneidman, Elad

    2013-01-01

    Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model—a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population. PMID:23516339

  12. Insights Into the Robustness of Minimum Error Entropy Estimation.

    PubMed

    Chen, Badong; Xing, Lei; Xu, Bin; Zhao, Haiquan; Principe, Jose C

    2016-12-22

    The minimum error entropy (MEE) is an important and highly effective optimization criterion in information theoretic learning (ITL). For regression problems, MEE aims at minimizing the entropy of the prediction error such that the estimated model preserves the information of the data generating system as much as possible. In many real world applications, the MEE estimator can outperform significantly the well-known minimum mean square error (MMSE) estimator and show strong robustness to noises especially when data are contaminated by non-Gaussian (multimodal, heavy tailed, discrete valued, and so on) noises. In this brief, we present some theoretical results on the robustness of MEE. For a one-parameter linear errors-in-variables (EIV) model and under some conditions, we derive a region that contains the MEE solution, which suggests that the MEE estimate can be very close to the true value of the unknown parameter even in presence of arbitrarily large outliers in both input and output variables. Theoretical prediction is verified by an illustrative example.

  13. Structural information in two-dimensional patterns: entropy convergence and excess entropy.

    PubMed

    Feldman, David P; Crutchfield, James P

    2003-05-01

    We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies. We show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension. We compare and contrast entropy convergence with mutual-information and structure-factor techniques for quantifying and detecting spatial structure.

  14. On multiscale entropy analysis for physiological data

    NASA Astrophysics Data System (ADS)

    Thuraisingham, Ranjit A.; Gottwald, Georg A.

    2006-07-01

    We perform an analysis of cardiac data using multiscale entropy as proposed in Costa et al. [Multiscale entropy analysis of complex physiological time series, Phys. Rev. Lett. 89 (2002) 068102]. We reproduce the signatures of the multiscale entropy for the three cases of young healthy hearts, atrial fibrillation and congestive heart failure. We show that one has to be cautious how to interpret these signatures in terms of the underlying dynamics. In particular, we show that different dynamical systems can exhibit the same signatures depending on the sampling time, and that similar systems may have different signatures depending on the time scales involved. Besides the total amount of data we identify the sampling time, the correlation time and the period of possible nonlinear oscillations as important time scales which have to be involved in a detailed analysis of the signatures of multiscale entropies. We illustrate our ideas with the Lorenz equation as a simple deterministic chaotic system.

  15. Entropy growth in emotional online dialogues

    NASA Astrophysics Data System (ADS)

    Sienkiewicz, J.; Skowron, M.; Paltoglou, G.; Hołyst, Janusz A.

    2013-02-01

    We analyze emotionally annotated massive data from IRC (Internet Relay Chat) and model the dialogues between its participants by assuming that the driving force for the discussion is the entropy growth of emotional probability distribution.

  16. α-z-Rényi relative entropies

    SciTech Connect

    Audenaert, Koenraad M. R.; Datta, Nilanjana

    2015-02-15

    We consider a two-parameter family of Rényi relative entropies D{sub α,z}(ρ ∥ σ) that are quantum generalisations of the classical Rényi divergence D{sub α}(p ∥ q). This family includes many known relative entropies (or divergences) such as the quantum relative entropy, the recently defined quantum Rényi divergences, as well as the quantum Rényi relative entropies. All its members satisfy the quantum generalizations of Rényi’s axioms for a divergence. We consider the range of the parameters α, z for which the data-processing inequality holds. We also investigate a variety of limiting cases for the two parameters, obtaining explicit formulas for each one of them.

  17. Hard sphere study of condensation entropy

    NASA Astrophysics Data System (ADS)

    Graziano, Giuseppe

    2008-06-01

    A simple procedure is devised to calculate the Ben-Naim standard condensation entropy by treating neat liquids as hard sphere fluids. The calculated values are close to the experimental ones for nonpolar liquids, but not for polar aprotic ones and for H-bonded liquids. For the latter the calculated entropy values become close to the experimental ones if the molecular van der Waals diameters are used instead of the effective ones. This implies that the magnitude of the orientational entropy loss due to H-bond formation is quantitatively similar to that of the configurational entropy gain for the decrease in excluded volume due to the bunching up effect caused by H-bonds.

  18. Lethality and entropy of protein interaction networks.

    PubMed

    Manke, Thomas; Demetrius, Lloyd; Vingron, Martin

    2005-01-01

    We characterize protein interaction networks in terms of network entropy. This approach suggests a ranking principle, which strongly correlates with elements of functional importance, such as lethal proteins. Our combined analysis of protein interaction networks and functional profiles in single cellular yeast and multi-cellular worm shows that proteins with large contribution to network entropy are preferentially lethal. While entropy is inherently a dynamical concept, the present analysis incorporates only structural information. Our result therefore highlights the importance of topological features, which appear as correlates of an underlying dynamical property, and which in turn determine functional traits. We argue that network entropy is a natural extension of previously studied observables, such as pathway multiplicity and centrality. It is also applicable to networks in which the processes can be quantified and therefore serves as a link to study questions of structural and dynamical robustness in a unified way.

  19. Generalized entropies and the similarity of texts

    NASA Astrophysics Data System (ADS)

    Altmann, Eduardo G.; Dias, Laércio; Gerlach, Martin

    2017-01-01

    We show how generalized Gibbs–Shannon entropies can provide new insights on the statistical properties of texts. The universal distribution of word frequencies (Zipf’s law) implies that the generalized entropies, computed at the word level, are dominated by words in a specific range of frequencies. Here we show that this is the case not only for the generalized entropies but also for the generalized (Jensen–Shannon) divergences, used to compute the similarity between different texts. This finding allows us to identify the contribution of specific words (and word frequencies) for the different generalized entropies and also to estimate the size of the databases needed to obtain a reliable estimation of the divergences. We test our results in large databases of books (from the google n-gram database) and scientific papers (indexed by Web of Science).

  20. Entropy and order in urban street networks

    PubMed Central

    Gudmundsson, Agust; Mohajeri, Nahid

    2013-01-01

    Many complex networks erase parts of their geometry as they develop, so that their evolution is difficult to quantify and trace. Here we introduce entropy measures for quantifying the complexity of street orientations and length variations within planar networks and apply them to the street networks of 41 British cities, whose geometric evolution over centuries can be explored. The results show that the street networks of the old central parts of the cities have lower orientation/length entropies - the streets are more tightly ordered and form denser networks - than the outer and more recent parts. Entropy and street length increase, because of spreading, with distance from the network centre. Tracing the 400-year evolution of one network indicates growth through densification (streets are added within the existing network) and expansion (streets are added at the margin of the network) and a gradual increase in entropy over time. PMID:24281305

  1. Group entropies, correlation laws, and zeta functions

    NASA Astrophysics Data System (ADS)

    Tempesta, Piergiulio

    2011-08-01

    The notion of group entropy is proposed. It enables the unification and generaliztion of many different definitions of entropy known in the literature, such as those of Boltzmann-Gibbs, Tsallis, Abe, and Kaniadakis. Other entropic functionals are introduced, related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium when the dynamics is weakly chaotic. The associated thermostatistics are discussed. The mathematical structure underlying our construction is that of formal group theory, which provides the general structure of the correlations among particles and dictates the associated entropic functionals. As an example of application, the role of group entropies in information theory is illustrated and generalizations of the Kullback-Leibler divergence are proposed. A new connection between statistical mechanics and zeta functions is established. In particular, Tsallis entropy is related to the classical Riemann zeta function.

  2. Tissue Radiation Response with Maximum Tsallis Entropy

    SciTech Connect

    Sotolongo-Grau, O.; Rodriguez-Perez, D.; Antoranz, J. C.; Sotolongo-Costa, Oscar

    2010-10-08

    The expression of survival factors for radiation damaged cells is currently based on probabilistic assumptions and experimentally fitted for each tumor, radiation, and conditions. Here, we show how the simplest of these radiobiological models can be derived from the maximum entropy principle of the classical Boltzmann-Gibbs expression. We extend this derivation using the Tsallis entropy and a cutoff hypothesis, motivated by clinical observations. The obtained expression shows a remarkable agreement with the experimental data found in the literature.

  3. Tissue radiation response with maximum Tsallis entropy.

    PubMed

    Sotolongo-Grau, O; Rodríguez-Pérez, D; Antoranz, J C; Sotolongo-Costa, Oscar

    2010-10-08

    The expression of survival factors for radiation damaged cells is currently based on probabilistic assumptions and experimentally fitted for each tumor, radiation, and conditions. Here, we show how the simplest of these radiobiological models can be derived from the maximum entropy principle of the classical Boltzmann-Gibbs expression. We extend this derivation using the Tsallis entropy and a cutoff hypothesis, motivated by clinical observations. The obtained expression shows a remarkable agreement with the experimental data found in the literature.

  4. Maximum entropy production - Full steam ahead

    NASA Astrophysics Data System (ADS)

    Lorenz, Ralph D.

    2012-05-01

    The application of a principle of Maximum Entropy Production (MEP, or less ambiguously MaxEP) to planetary climate is discussed. This idea suggests that if sufficiently free of dynamical constraints, the atmospheric and oceanic heat flows across a planet may conspire to maximize the generation of mechanical work, or entropy. Thermodynamic and information-theoretic aspects of this idea are discussed. These issues are also discussed in the context of dust devils, convective vortices found in strongly-heated desert areas.

  5. Carnot to Clausius: caloric to entropy

    NASA Astrophysics Data System (ADS)

    Newburgh, Ronald

    2009-07-01

    This paper discusses how the Carnot engine led to the formulation of the second law of thermodynamics and entropy. The operation of the engine is analysed both in terms of heat as the caloric fluid and heat as a form of energy. A keystone of Carnot's thinking was the absolute conservation of caloric. Although the Carnot analysis was partly incorrect, Clausius showed that by reinterpreting Carnot's caloric as entropy he was able to formulate the second law.

  6. Up-hill diffusion, creation of density gradients: Entropy measure for systems with topological constraints

    NASA Astrophysics Data System (ADS)

    Sato, N.; Yoshida, Z.

    2016-06-01

    It is always some constraint that yields any nontrivial structure from statistical averages. As epitomized by the Boltzmann distribution, the energy conservation is often the principal constraint acting on mechanical systems. Here we investigate a different type: the topological constraint imposed on "space." Such a constraint emerges from the null space of the Poisson operator linking an energy gradient to phase space velocity and appears as an adiabatic invariant altering the preserved phase space volume at the core of statistical mechanics. The correct measure of entropy, built on the distorted invariant measure, behaves consistently with the second law of thermodynamics. The opposite behavior (decreasing entropy and negative entropy production) arises in arbitrary coordinates. An ensemble of rotating rigid bodies is worked out. The theory is then applied to up-hill diffusion in a magnetosphere.

  7. Thresholding schemes for visible light communications with CMOS camera using entropy-based algorithms.

    PubMed

    Liang, Kevin; Chow, Chi-Wai; Liu, Yang; Yeh, Chien-Hung

    2016-10-31

    Recent visible light communication (VLC) studies mainly used positive-intrinsic-negative (PIN) and avalanche photodiode (APD). VLC using embedded complementary-metal-oxide-semiconductor (CMOS) camera is attractive. Using the rolling shutter effect of CMOS camera can increase the VLC data rate; and different techniques have been proposed for improving the demodulation of the rolling shutter pattern. Important steps to demodulate the rolling shutter pattern are the smoothing and the application of efficient thresholding to distinguish data logic. Here, we propose and demonstrate for the first time two entropy thresholding algorithms, including maximum entropy thresholding and minimum cross entropy thresholding. Experimental evaluation to compare their bit-error-rate (BER) performances and efficiencies are also performed.

  8. Entropies and correlations in classical and quantum systems

    NASA Astrophysics Data System (ADS)

    Man'ko, Margarita A.; Man'ko, Vladimir I.; Marmo, Giuseppe

    2016-09-01

    We present a review of entropy properties for classical and quantum systems including Shannon entropy, von Neumann entropy, Rényi entropy, and Tsallis entropy. We discuss known and new entropic and information inequalities for classical and quantum systems, both composite and noncomposite. We demonstrate matrix inequalities associated with the entropic subadditivity and strong subadditivity conditions and give a new inequality for matrix elements of unitary matrices.

  9. Input management of production systems.

    PubMed

    Odum, E P

    1989-01-13

    Nonpoint sources of pollution, which are largely responsible for stressing regional and global life-supporting atmosphere, soil, and water, can only be reduced (and ultimately controlled) by input management that involves increasing the efficiency of production systems and reducing the inputs of environmentally damaging materials. Input management requires a major change, an about-face, in the approach to management of agriculture, power plants, and industries because the focus is on waste reduction and recycling rather than on waste disposal. For large-scale ecosystem-level situations a top-down hierarchical approach is suggested and illustrated by recent research in agroecology and landscape ecology.

  10. Continuously differentiable sample-spacing entropy estimation.

    PubMed

    Ozertem, Umut; Uysal, Ismail; Erdogmus, Deniz

    2008-11-01

    The insufficiency of using only second-order statistics and premise of exploiting higher order statistics of the data has been well understood, and more advanced objectives including higher order statistics, especially those stemming from information theory, such as error entropy minimization, are now being studied and applied in many contexts of machine learning and signal processing. In the adaptive system training context, the main drawback of utilizing output error entropy as compared to correlation-estimation-based second-order statistics is the computational load of the entropy estimation, which is usually obtained via a plug-in kernel estimator. Sample-spacing estimates offer computationally inexpensive entropy estimators; however, resulting estimates are not differentiable, hence, not suitable for gradient-based adaptation. In this brief paper, we propose a nonparametric entropy estimator that captures the desirable properties of both approaches. The resulting estimator yields continuously differentiable estimates with a computational complexity at the order of those of the sample-spacing techniques. The proposed estimator is compared with the kernel density estimation (KDE)-based entropy estimator in the supervised neural network training framework with computation time and performance comparisons.

  11. Normalized entropy measure for multimodality image alignment

    NASA Astrophysics Data System (ADS)

    Studholme, Colin; Hawkes, David J.; Hill, Derek L.

    1998-06-01

    Automated multi-modality 3D medical image alignment has been an active area of research for many years. There have been a number of recent papers proposing and investigating the use of entropy derived measures of brain image alignment. Any registration measure must allow us to choose between transformation estimates based on the similarity of images within their volume of overlap. Since 3D medical images often have a limited extent and overlap, the similarity measure for the two transformation estimates may be derived from two very different regions within the images. Direct measures of information such as the joint entropy and mutual information will therefore be a function of, not only image similarity in the region of overlap, but also of the local image content within the overlap. In this paper we present a new measure, normalized mutual information, which is simply the ratio of the sum of the marginal entropies and the joint entropy. The effect of changing overlap on current entropy measures and this normalized measure are compared using a simple image model and experiments on clinical MR-PET and MR-CT image data. Results indicate that the normalized entropy measure provides significantly improved behavior over a range of imaged fields of view.

  12. Remarks on entanglement entropy for gauge fields

    NASA Astrophysics Data System (ADS)

    Casini, Horacio; Huerta, Marina; Rosabal, José Alejandro

    2014-04-01

    In gauge theories the presence of constraints can obstruct expressing the global Hilbert space as a tensor product of the Hilbert spaces corresponding to degrees of freedom localized in complementary regions. In algebraic terms, this is due to the presence of a center—a set of operators which commute with all others—in the gauge invariant operator algebra corresponding to a finite region. A unique entropy can be assigned to algebras with a center, giving a place to a local entropy in lattice gauge theories. However, ambiguities arise on the correspondence between algebras and regions. In particular, it is always possible to choose (in many different ways) local algebras with a trivial center, and hence a genuine entanglement entropy, for any region. These choices are in correspondence with maximal trees of links on the boundary, which can be interpreted as partial gauge fixings. This interpretation entails a gauge fixing dependence of the entanglement entropy. In the continuum limit, however, ambiguities in the entropy are given by terms local on the boundary of the region, in such a way relative entropy and mutual information are finite, universal, and gauge independent quantities.

  13. Improved entropy rate estimation in physiological data.

    PubMed

    Lake, D E

    2011-01-01

    Calculating entropy rate in physiologic signals has proven very useful in many settings. Common entropy estimates for this purpose are sample entropy (SampEn) and its less robust elder cousin, approximate entropy (ApEn). Both approaches count matches within a tolerance r for templates of length m consecutive observations. When physiologic data records are long and well-behaved, both approaches work very well for a wide range of m and r. However, more attention to the details of the estimation algorithm is needed for short records and signals with anomalies. In addition, interpretation of the magnitude of these estimates is highly dependent on how r is chosen and precludes comparison across studies with even slightly different methodologies. In this paper, we summarize recent novel approaches to improve the accuracy of entropy estimation. An important (but not necessarily new) alternative to current approaches is to develop estimates that convert probabilities to densities by normalizing by the matching region volume. This approach leads to a novel concept introduced here of reporting entropy rate in equivalent Gaussian white noise units. Another approach is to allow r to vary so that a pre-specified number of matches are found, called the minimum numerator count, to ensure confident probability estimation. The approaches are illustrated using a simple example of detecting abnormal cardiac rhythms in heart rate records.

  14. Wavelet Packet Entropy for Heart Murmurs Classification

    PubMed Central

    Safara, Fatemeh; Doraisamy, Shyamala; Azman, Azreen; Jantan, Azrul; Ranga, Sri

    2012-01-01

    Heart murmurs are the first signs of cardiac valve disorders. Several studies have been conducted in recent years to automatically differentiate normal heart sounds, from heart sounds with murmurs using various types of audio features. Entropy was successfully used as a feature to distinguish different heart sounds. In this paper, new entropy was introduced to analyze heart sounds and the feasibility of using this entropy in classification of five types of heart sounds and murmurs was shown. The entropy was previously introduced to analyze mammograms. Four common murmurs were considered including aortic regurgitation, mitral regurgitation, aortic stenosis, and mitral stenosis. Wavelet packet transform was employed for heart sound analysis, and the entropy was calculated for deriving feature vectors. Five types of classification were performed to evaluate the discriminatory power of the generated features. The best results were achieved by BayesNet with 96.94% accuracy. The promising results substantiate the effectiveness of the proposed wavelet packet entropy for heart sounds classification. PMID:23227043

  15. Entropy Transfer of Quantum Gravity Information Processing

    NASA Astrophysics Data System (ADS)

    Gyongyosi, Laszlo; Imre, Sandor

    2015-05-01

    We introduce the term smooth entanglement entropy transfer, a phenomenon that is a consequence of the causality-cancellation property of the quantum gravity environment. The causality-cancellation of the quantum gravity space removes the causal dependencies of the local systems. We study the physical effects of the causality-cancellation and show that it stimulates entropy transfer between the quantum gravity environment and the independent local systems of the quantum gravity space. The entropy transfer reduces the entropies of the contributing local systems and increases the entropy of the quantum gravity environment. We discuss the space-time geometry structure of the quantum gravity environment and the local quantum systems. We propose the space-time geometry model of the smooth entropy transfer. We reveal on a smooth Cauchy slice that the space-time geometry of the quantum gravity environment dynamically adapts to the vanishing causality. We prove that the Cauchy area expansion, along with the dilation of the Rindler horizon area of the quantum gravity environment, is a corollary of the causality-cancellation of the quantum gravity environment. This work was partially supported by the GOP-1.1.1-11-2012-0092 (Secure quantum key distribution between two units on optical fiber network) project sponsored by the EU and European Structural Fund, and by the COST Action MP1006.

  16. Entanglement entropy and nonabelian gauge symmetry

    NASA Astrophysics Data System (ADS)

    Donnelly, William

    2014-11-01

    Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang-Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity.

  17. Mechanical Entropy and Its Implications

    NASA Astrophysics Data System (ADS)

    Williams, Pharis E.

    2001-09-01

    It is shown that the classical laws of thermodynamics require that mechanical systems must exhibit energy that becomes unavailable to do useful work. In thermodynamics, this type of energy is called entropy. It is further shown that these laws require two metrical manifolds, equations of motion, field equations, and Weyl's quantum principles. Weyl's quantum principle requires quantization of the electrostatic potential of a particle and that this potential be non-singular. The interactions of particles through these non-singular electrostatic potentials are analyzed in the low velocity limit and in the relativistic limit. It is shown that writing the two particle interactions for unlike particles allows an examination in two limiting cases: large and small separations. These limits are shown to have the limiting motions of: all motions are ABOUT the center of mass or all motion is OF the center of mass. The first limit leads to the standard Dirac equation. The second limit is shown to have equations of which the electroweak theory is a subset. An extension of the gauge principle into a five-dimensional manifold, then restricting the generality of the five-dimensional manifold by using the conservation principle, shows that the four-dimensional hypersurface that is embedded within the 5-D manifold is required to obey Einstein's field equations. The 5-D gravitational quantum equations of the solar system are presented.

  18. Maximum entropy production in daisyworld

    NASA Astrophysics Data System (ADS)

    Maunu, Haley A.; Knuth, Kevin H.

    2012-05-01

    Daisyworld was first introduced in 1983 by Watson and Lovelock as a model that illustrates how life can influence a planet's climate. These models typically involve modeling a planetary surface on which black and white daisies can grow thus influencing the local surface albedo and therefore also the temperature distribution. Since then, variations of daisyworld have been applied to study problems ranging from ecological systems to global climate. Much of the interest in daisyworld models is due to the fact that they enable one to study self-regulating systems. These models are nonlinear, and as such they exhibit sensitive dependence on initial conditions, and depending on the specifics of the model they can also exhibit feedback loops, oscillations, and chaotic behavior. Many daisyworld models are thermodynamic in nature in that they rely on heat flux and temperature gradients. However, what is not well-known is whether, or even why, a daisyworld model might settle into a maximum entropy production (MEP) state. With the aim to better understand these systems, this paper will discuss what is known about the role of MEP in daisyworld models.

  19. Entropy and the Magic Flute

    NASA Astrophysics Data System (ADS)

    Morowitz, Harold J.

    1996-10-01

    Harold Morowitz has long been highly regarded both as an eminent scientist and as an accomplished science writer. The essays in The Wine of Life , his first collection, were hailed by C.P. Snow as "some of the wisest, wittiest and best informed I have ever read," and Carl Sagan called them "a delight to read." In later volumes he established a reputation for a wide-ranging intellect, an ability to see unexpected connections and draw striking parallels, and a talent for communicating scientific ideas with optimism and wit. With Entropy and the Magic Flute , Morowitz once again offers an appealing mix of brief reflections on everything from litmus paper to the hippopotamus to the sociology of Palo Alto coffee shops. Many of these pieces are appreciations of scientists that Morowitz holds in high regard, while others focus on health issues, such as America's obsession with cheese toppings. There is also a fascinating piece on the American Type Culture Collection, a zoo or warehouse for microbes that houses some 11,800 strains of bacteria, and over 3,000 specimens of protozoa, algae, plasmids, and oncogenes. Here then are over forty light, graceful essays in which one of our wisest experimental biologists comments on issues of science, technology, society, philosophy, and the arts.

  20. Entanglement entropy of electronic excitations

    NASA Astrophysics Data System (ADS)

    Plasser, Felix

    2016-05-01

    A new perspective into correlation effects in electronically excited states is provided through quantum information theory. The entanglement between the electron and hole quasiparticles is examined, and it is shown that the related entanglement entropy can be computed from the eigenvalue spectrum of the well-known natural transition orbital (NTO) decomposition. Non-vanishing entanglement is obtained whenever more than one NTO pair is involved, i.e., in the case of a multiconfigurational or collective excitation. An important implication is that in the case of entanglement it is not possible to gain a complete description of the state character from the orbitals alone, but more specific analysis methods are required to decode the mutual information between the electron and hole. Moreover, the newly introduced number of entangled states is an important property by itself giving information about excitonic structure. The utility of the formalism is illustrated in the cases of the excited states of two interacting ethylene molecules, the conjugated polymer para-phenylene vinylene, and the naphthalene molecule.

  1. Entropy-Driven Cutoff Phenomena

    NASA Astrophysics Data System (ADS)

    Lancia, Carlo; Nardi, Francesca R.; Scoppola, Benedetto

    2012-10-01

    In this paper we present, in the context of Diaconis' paradigm, a general method to detect the cutoff phenomenon. We use this method to prove cutoff in a variety of models, some already known and others not yet appeared in literature, including a non-reversible random walk on a cylindrical lattice. All the given examples clearly indicate that a drift towards the opportune quantiles of the stationary measure could be held responsible for this phenomenon. In the case of birth-and-death chains this mechanism is fairly well understood; our work is an effort to generalize this picture to more general systems, such as systems having stationary measure spread over the whole state space or systems in which the study of the cutoff may not be reduced to a one-dimensional problem. In those situations the drift may be looked for by means of a suitable partitioning of the state space into classes; using a statistical mechanics language it is then possible to set up a kind of energy-entropy competition between the weight and the size of the classes. Under the lens of this partitioning one can focus the mentioned drift and prove cutoff with relative ease.

  2. Min-entropy and quantum key distribution: Nonzero key rates for ''small'' numbers of signals

    SciTech Connect

    Bratzik, Sylvia; Mertz, Markus; Kampermann, Hermann; Bruss, Dagmar

    2011-02-15

    We calculate an achievable secret key rate for quantum key distribution with a finite number of signals by evaluating the quantum conditional min-entropy explicitly. The min-entropy for a classical random variable is the negative logarithm of the maximal value in its probability distribution. The quantum conditional min-entropy can be expressed in terms of the guessing probability, which we calculate for d-dimensional systems. We compare these key rates to previous approaches using the von Neumann entropy and find nonzero key rates for a smaller number of signals. Furthermore, we improve the secret key rates by modifying the parameter estimation step. Both improvements taken together lead to nonzero key rates for only 10{sup 4}-10{sup 5} signals. An interesting conclusion can also be drawn from the additivity of the min-entropy and its relation to the guessing probability: for a set of symmetric tensor product states, the optimal minimum-error discrimination (MED) measurement is the optimal MED measurement on each subsystem.

  3. Intra-tumour signalling entropy determines clinical outcome in breast and lung cancer.

    PubMed

    Banerji, Christopher R S; Severini, Simone; Caldas, Carlos; Teschendorff, Andrew E

    2015-03-01

    The cancer stem cell hypothesis, that a small population of tumour cells are responsible for tumorigenesis and cancer progression, is becoming widely accepted and recent evidence has suggested a prognostic and predictive role for such cells. Intra-tumour heterogeneity, the diversity of the cancer cell population within the tumour of an individual patient, is related to cancer stem cells and is also considered a potential prognostic indicator in oncology. The measurement of cancer stem cell abundance and intra-tumour heterogeneity in a clinically relevant manner however, currently presents a challenge. Here we propose signalling entropy, a measure of signalling pathway promiscuity derived from a sample's genome-wide gene expression profile, as an estimate of the stemness of a tumour sample. By considering over 500 mixtures of diverse cellular expression profiles, we reveal that signalling entropy also associates with intra-tumour heterogeneity. By analysing 3668 breast cancer and 1692 lung adenocarcinoma samples, we further demonstrate that signalling entropy correlates negatively with survival, outperforming leading clinical gene expression based prognostic tools. Signalling entropy is found to be a general prognostic measure, valid in different breast cancer clinical subgroups, as well as within stage I lung adenocarcinoma. We find that its prognostic power is driven by genes involved in cancer stem cells and treatment resistance. In summary, by approximating both stemness and intra-tumour heterogeneity, signalling entropy provides a powerful prognostic measure across different epithelial cancers.

  4. Optimization of floodplain monitoring sensors through an entropy approach

    NASA Astrophysics Data System (ADS)

    Ridolfi, E.; Yan, K.; Alfonso, L.; Di Baldassarre, G.; Napolitano, F.; Russo, F.; Bates, P. D.

    2012-04-01

    To support the decision making processes of flood risk management and long term floodplain planning, a significant issue is the availability of data to build appropriate and reliable models. Often the required data for model building, calibration and validation are not sufficient or available. A unique opportunity is offered nowadays by the globally available data, which can be freely downloaded from internet. However, there remains the question of what is the real potential of those global remote sensing data, characterized by different accuracies, for global inundation monitoring and how to integrate them with inundation models. In order to monitor a reach of the River Dee (UK), a network of cheap wireless sensors (GridStix) was deployed both in the channel and in the floodplain. These sensors measure the water depth, supplying the input data for flood mapping. Besides their accuracy and reliability, their location represents a big issue, having the purpose of providing as much information as possible and at the same time as low redundancy as possible. In order to update their layout, the initial number of six sensors has been increased up to create a redundant network over the area. Through an entropy approach, the most informative and the least redundant sensors have been chosen among all. First, a simple raster-based inundation model (LISFLOOD-FP) is used to generate a synthetic GridStix data set of water stages. The Digital Elevation Model (DEM) used for hydraulic model building is the globally and freely available SRTM DEM. Second, the information content of each sensor has been compared by evaluating their marginal entropy. Those with a low marginal entropy are excluded from the process because of their low capability to provide information. Then the number of sensors has been optimized considering a Multi-Objective Optimization Problem (MOOP) with two objectives, namely maximization of the joint entropy (a measure of the information content) and

  5. System monitors discrete computer inputs

    NASA Technical Reports Server (NTRS)

    Burns, J. J.

    1966-01-01

    Computer system monitors inputs from checkout devices. The comparing, addressing, and controlling functions are performed in the I/O unit. This leaves the computer main frame free to handle memory, access priority, and interrupt instructions.

  6. Minimum relative entropy, Bayes and Kapur

    NASA Astrophysics Data System (ADS)

    Woodbury, Allan D.

    2011-04-01

    The focus of this paper is to illustrate important philosophies on inversion and the similarly and differences between Bayesian and minimum relative entropy (MRE) methods. The development of each approach is illustrated through the general-discrete linear inverse. MRE differs from both Bayes and classical statistical methods in that knowledge of moments are used as ‘data’ rather than sample values. MRE like Bayes, presumes knowledge of a prior probability distribution and produces the posterior pdf itself. MRE attempts to produce this pdf based on the information provided by new moments. It will use moments of the prior distribution only if new data on these moments is not available. It is important to note that MRE makes a strong statement that the imposed constraints are exact and complete. In this way, MRE is maximally uncommitted with respect to unknown information. In general, since input data are known only to within a certain accuracy, it is important that any inversion method should allow for errors in the measured data. The MRE approach can accommodate such uncertainty and in new work described here, previous results are modified to include a Gaussian prior. A variety of MRE solutions are reproduced under a number of assumed moments and these include second-order central moments. Various solutions of Jacobs & van der Geest were repeated and clarified. Menke's weighted minimum length solution was shown to have a basis in information theory, and the classic least-squares estimate is shown as a solution to MRE under the conditions of more data than unknowns and where we utilize the observed data and their associated noise. An example inverse problem involving a gravity survey over a layered and faulted zone is shown. In all cases the inverse results match quite closely the actual density profile, at least in the upper portions of the profile. The similar results to Bayes presented in are a reflection of the fact that the MRE posterior pdf, and its mean

  7. Maximum entropy principal for transportation

    SciTech Connect

    Bilich, F.; Da Silva, R.

    2008-11-06

    In this work we deal with modeling of the transportation phenomenon for use in the transportation planning process and policy-impact studies. The model developed is based on the dependence concept, i.e., the notion that the probability of a trip starting at origin i is dependent on the probability of a trip ending at destination j given that the factors (such as travel time, cost, etc.) which affect travel between origin i and destination j assume some specific values. The derivation of the solution of the model employs the maximum entropy principle combining a priori multinomial distribution with a trip utility concept. This model is utilized to forecast trip distributions under a variety of policy changes and scenarios. The dependence coefficients are obtained from a regression equation where the functional form is derived based on conditional probability and perception of factors from experimental psychology. The dependence coefficients encode all the information that was previously encoded in the form of constraints. In addition, the dependence coefficients encode information that cannot be expressed in the form of constraints for practical reasons, namely, computational tractability. The equivalence between the standard formulation (i.e., objective function with constraints) and the dependence formulation (i.e., without constraints) is demonstrated. The parameters of the dependence-based trip-distribution model are estimated, and the model is also validated using commercial air travel data in the U.S. In addition, policy impact analyses (such as allowance of supersonic flights inside the U.S. and user surcharge at noise-impacted airports) on air travel are performed.

  8. Quantum statistical entropy for Kerr de Sitter black hole

    NASA Astrophysics Data System (ADS)

    Zhang, Li-Chun; Wu, Yue-Qin; Zhao, Ren

    2004-06-01

    Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n+2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black hole's entropy which contains two horizons (a black hole's horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole's horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black hole's entropy and horizon's area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.

  9. Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

    NASA Astrophysics Data System (ADS)

    Xu, Kaixuan; Wang, Jun

    2017-02-01

    In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model.

  10. Substorm onset: A switch on the sequence of transport from decreasing entropy to increasing entropy

    NASA Astrophysics Data System (ADS)

    Chen, C. X.

    2016-05-01

    In this study, we propose a scenario about the trigger for substorm onset. In a stable magnetosphere, entropy is an increasing function tailward. However, in the growth phase of a substorm, a later born bubble has lower entropy than earlier born bubbles. When a bubble arrives at its final destination in the near-Earth region, it will spread azimuthally because of its relatively uniform entropy. The magnetic flux tubes of a dying bubble, which cause the most equatorward aurora thin arc, would block the later coming bubble tailward of them, forming an unstable domain. Therefore, an interchange instability develops, which leads to the collapse of the unstable domain, followed by the collapse of the stretched plasma sheet. We regard the substorm onset as a switch on the sequence of transport, i.e., from a decreasing entropy process to an increasing entropy process. We calculated the most unstable growth rates and the wavelengths of instability, and both are in agreement with observations.

  11. Negative pressures and melting point depression in oxide-coated liquid metal droplets

    NASA Technical Reports Server (NTRS)

    Spaepen, F.; Turnbull, D.

    1979-01-01

    Negative pressures and melting point depression in oxide-coated liquid metal droplets are studied. The calculation presented show the existence of large negative pressures when the oxide coating is thick enough. The change in the melting point caused by these negative pressures should be considered in studies of homogeneous crystal nucleation. Furthermore, since the negative pressure raises the entropy of the melt, it increases the entropy loss at the crystal-melt interface; the resulting increase of the surface tension could have a large effect on the homogeneous nucleation frequency.

  12. Entanglement negativity in the multiverse

    SciTech Connect

    Kanno, Sugumi; Soda, Jiro E-mail: jonathan.shock@uct.ac.za

    2015-03-01

    We explore quantum entanglement between two causally disconnected regions in the multiverse. We first consider a free massive scalar field, and compute the entanglement negativity between two causally separated open charts in de Sitter space. The qualitative feature of it turns out to be in agreement with that of the entanglement entropy. We then introduce two observers who determine the entanglement between two causally disconnected de Sitter spaces. When one of the observers remains constrained to a region of the open chart in a de Sitter space, we find that the scale dependence enters into the entanglement. We show that a state which is initially maximally entangled becomes more entangled or less entangled on large scales depending on the mass of the scalar field and recovers the initial entanglement in the small scale limit. We argue that quantum entanglement may provide some evidence for the existence of the multiverse.

  13. Entanglement negativity in the multiverse

    SciTech Connect

    Kanno, Sugumi; Shock, Jonathan P.; Soda, Jiro

    2015-03-10

    We explore quantum entanglement between two causally disconnected regions in the multiverse. We first consider a free massive scalar field, and compute the entanglement negativity between two causally separated open charts in de Sitter space. The qualitative feature of it turns out to be in agreement with that of the entanglement entropy. We then introduce two observers who determine the entanglement between two causally disconnected de Sitter spaces. When one of the observers remains constrained to a region of the open chart in a de Sitter space, we find that the scale dependence enters into the entanglement. We show that a state which is initially maximally entangled becomes more entangled or less entangled on large scales depending on the mass of the scalar field and recovers the initial entanglement in the small scale limit. We argue that quantum entanglement may provide some evidence for the existence of the multiverse.

  14. Spatial Decomposition of Translational Water-Water Correlation Entropy in Binding Pockets.

    PubMed

    Nguyen, Crystal N; Kurtzman, Tom; Gilson, Michael K

    2016-01-12

    A number of computational tools available today compute the thermodynamic properties of water at surfaces and in binding pockets by using inhomogeneous solvation theory (IST) to analyze explicit-solvent simulations. Such methods enable qualitative spatial mappings of both energy and entropy around a solute of interest and can also be applied quantitatively. However, the entropy estimates of existing methods have, to date, been almost entirely limited to the first-order terms in the IST's entropy expansion. These first-order terms account for localization and orientation of water molecules in the field of the solute but not for the modification of water-water correlations by the solute. Here, we present an extension of the Grid Inhomogeneous Solvation Theory (GIST) approach which accounts for water-water translational correlations. The method involves rewriting the two-point density of water in terms of a conditional density and utilizes the efficient nearest-neighbor entropy estimation approach. Spatial maps of this second order term, for water in and around the synthetic host cucurbit[7]uril and in the binding pocket of the enzyme Factor Xa, reveal mainly negative contributions, indicating solute-induced water-water correlations relative to bulk water; particularly strong signals are obtained for sites at the entrances of cavities or pockets. This second-order term thus enters with the same, negative, sign as the first order translational and orientational terms. Numerical and convergence properties of the methodology are examined.

  15. Spatial Decomposition of Translational Water–Water Correlation Entropy in Binding Pockets

    PubMed Central

    2015-01-01

    A number of computational tools available today compute the thermodynamic properties of water at surfaces and in binding pockets by using inhomogeneous solvation theory (IST) to analyze explicit-solvent simulations. Such methods enable qualitative spatial mappings of both energy and entropy around a solute of interest and can also be applied quantitatively. However, the entropy estimates of existing methods have, to date, been almost entirely limited to the first-order terms in the IST’s entropy expansion. These first-order terms account for localization and orientation of water molecules in the field of the solute but not for the modification of water–water correlations by the solute. Here, we present an extension of the Grid Inhomogeneous Solvation Theory (GIST) approach which accounts for water–water translational correlations. The method involves rewriting the two-point density of water in terms of a conditional density and utilizes the efficient nearest-neighbor entropy estimation approach. Spatial maps of this second order term, for water in and around the synthetic host cucurbit[7]uril and in the binding pocket of the enzyme Factor Xa, reveal mainly negative contributions, indicating solute-induced water–water correlations relative to bulk water; particularly strong signals are obtained for sites at the entrances of cavities or pockets. This second-order term thus enters with the same, negative, sign as the first order translational and orientational terms. Numerical and convergence properties of the methodology are examined. PMID:26636620

  16. Phonon anharmonicity and components of the entropy in palladium and platinum

    NASA Astrophysics Data System (ADS)

    Shen, Yang; Li, Chen W.; Tang, Xiaoli; Smith, Hillary L.; Fultz, B.

    2016-06-01

    Inelastic neutron scattering was used to measure the phonon density of states in fcc palladium and platinum metal at temperatures from 7 K to 1576 K. Both phonon-phonon interactions and electron-phonon interactions were calculated by methods based on density functional theory (DFT) and were consistent with the measured shifts and broadenings of phonons with temperature. Unlike the longitudinal modes, the characteristic transverse modes had a nonlinear dependence on temperature owing to the requirement for a population of thermal phonons for upscattering. Kohn anomalies were observed in the measurements at low temperature and were reproduced by calculations based on DFT. Contributions to the entropy from phonons and electrons were assessed and summed to obtain excellent agreement with prior calorimetric data. The entropy from thermal expansion is positive for both phonons and electrons but larger for phonons. The anharmonic phonon entropy is negative in Pt, but in Pd it changes from positive to negative with increasing temperature. Owing to the position of the Fermi level on the electronic DOS, the electronic entropy was sensitive to the adiabatic electron-phonon interaction in both Pd and Pt. The adiabatic EPI depended strongly on thermal atom displacements.

  17. Band target entropy minimization for retrieving the information of individual components from overlapping chromatographic data.

    PubMed

    Xia, Zhenzhen; Liu, Yan; Cai, Wensheng; Shao, Xueguang

    2015-09-11

    Band target entropy minimization (BTEM) is a self-modeling curve resolution (SMCR) approach relying on non-negative criterion and minimization of Shannon entropy. In this study, BTEM algorithm was applied to retrieving the information of individual components from overlapping gas chromatography-mass spectrometry (GC-MS) data. The algorithm starts with dividing the whole data into bands along the retention time. In each band, singular value decomposition (SVD) is used to decompose the data into scores and loadings. Because the pure chromatographic signal possesses the lowest Shannon entropy, the chromatographic signal of each component can be constructed by optimizing the combination of the loadings with minimal Shannon entropy under non-negative criterion. To show the efficiency of the algorithm, a simulated four-component overlapping GC-MS data and an experimental GC-MS data of 18 organophosphorus pesticide mixture are investigated. The results show that both the chromatographic profiles and mass spectra of the components can be successfully extracted from the overlapping signals.

  18. Maximum entropy production rate in quantum thermodynamics

    NASA Astrophysics Data System (ADS)

    Beretta, Gian Paolo

    2010-06-01

    In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schrödinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, a recent paper [Gheorghiu-Svirschevski 2001 Phys. Rev. A 63 054102] reproposes the nonlinear equation of motion proposed by the present author [see Beretta G P 1987 Found. Phys. 17 365 and references therein] for quantum (thermo)dynamics of a single isolated indivisible constituent system, such as a single particle, qubit, qudit, spin or atomic system, or a Bose-Einstein or Fermi-Dirac field. As already proved, such nonlinear dynamics entails a fundamental unifying microscopic proof and extension of Onsager's reciprocity and Callen's fluctuation-dissipation relations to all nonequilibrium states, close and far from thermodynamic equilibrium. In this paper we propose a brief but self-contained review of the main results already proved, including the explicit geometrical construction of the equation of motion from the steepest-entropy-ascent ansatz and its exact mathematical and conceptual equivalence with the maximal-entropy-generation variational-principle formulation presented in Gheorghiu-Svirschevski S 2001 Phys. Rev. A 63 022105. Moreover, we show how it can be extended to the case of a composite system to obtain the general form of the equation of motion, consistent with the demanding requirements of strong separability and of compatibility with general thermodynamics principles. The irreversible term in the equation of motion describes the spontaneous attraction of the state operator in the direction of steepest entropy ascent, thus implementing the maximum entropy production principle in quantum theory. The time rate at which the path of steepest entropy ascent is followed has so far been left unspecified. As a step towards the identification of such rate, here we propose a possible, well

  19. [Identification of coupling relationship between urbanization and ecological environment in Jilin from entropy change perspective].

    PubMed

    Sun, Ping-Jun; Xiu, Chun-Liang; Zhang, Tian-Jiao

    2014-03-01

    By using the entropy change equation of the second law of thermodynamics, entropy method and PSE model, this article made an analysis on coupling relationship between urbanization and ecological environment in Jilin Province from 2001 to 2011. In the study period, the urbanization development had been out of normal evolution track: The economic urbanization and space urbanization dominated the whole urbanization process, while population urbanization was neglected too seriously, with an apparent characteristic of extensive and inefficient input of resources (especially land resource). According to the levels of ecological environment on the basis of PSE model, not only the pressure index, sensitivity index and the elasticity index, but also the comprehensive index showed considerable growth with obvious stage characteristics: ascending-descending-ascending. The total entropy values of the urbanization were less than zero during the time, which meant an unstable rising curve. While the total trophy values of the ecological environment varied below and above zero, and 2003, 2006, 2010 and 2011 were the "turning points", reflecting the instability of the ecological environment. The coupling total entropy values between urbanization and ecological environment had the same characteristics with the ecological environment: the same "turning points" and shape of the curve, in which, the "turning points" corresponded to the type of antagonistic evolution pattern, while the rest of years responded to the type of coordination evolution pattern.

  20. Constraining the mSUGRA parameter space through entropy and abundance criteria

    SciTech Connect

    Cabral-Rosetti, Luis G.; Mondragon, Myriam; Nunez, Dario; Sussman, Roberto A.; Zavala, Jesus; Nellen, Lukas

    2007-06-19

    We explore the use of two criteria to constrain the allowed parameter space in mSUGRA models; both criteria are based in the calculation of the present density of neutralinos {chi}0 as Dark Matter in the Universe. The first one is the usual ''abundance'' criterion that requieres that present neutralino relic density complies with 0.0945 < {omega}CDMh2 < 0.1287, which are the 2{sigma} bounds according to WMAP. To calculate the relic density we use the public numerical code micrOMEGAS. The second criterion is the original idea presented in [3] that basically applies the microcanonical definition of entropy to a weakly interacting and self-gravitating gas, and then evaluate the change in entropy per particle of this gas between the freeze-out era and present day virialized structures. An 'entropy consistency' criterion emerges by comparing theoretical and empirical estimates of this entropy. One of the objetives of the work is to analyze the joint application of both criteria, already done in [3], to see if their results, using approximations for the calculations of the relic density, agree with the results coming from the exact numerical results of micrOMEGAS. The main objetive of the work is to use this method to constrain the parameter space in mSUGRA models that are inputs for the calculations of micrOMEGAS, and thus to get some bounds on the predictions for the SUSY spectra.

  1. Monitoring the depth of anesthesia using entropy features and an artificial neural network.

    PubMed

    Shalbaf, Reza; Behnam, Hamid; Sleigh, Jamie W; Steyn-Ross, Alistair; Voss, Logan J

    2013-08-15

    Monitoring the depth of anesthesia using an electroencephalogram (EEG) is a major ongoing challenge for anesthetists. The EEG is a recording of brain electrical activity, and it contains valuable information related to the different physiological states of the brain. This study proposes a novel automated method consisting of two steps for assessing anesthesia depth. Initially, the sample entropy and permutation entropy features were extracted from the EEG signal. Because EEG-derived parameters represent different aspects of the EEG features, it would be reasonable to use multiple parameters to assess the effect of the anesthetic. The sample entropy and permutation entropy features quantified the amount of complexity or irregularity in the EEG data and were conceptually simple, computationally efficient and artifact-resistant. Next, the extracted features were used as input for an artificial neural network, which was a data processing system based on the structure of a biological nervous system. The experimental results indicated that an overall accuracy of 88% could be obtained during sevoflurane anesthesia in 17 patients to classify the EEG data into awake, light, general and deep anesthetized states. In addition, this method yielded a classification accuracy of 92.4% to distinguish between awake and general anesthesia in an independent database of propofol and desflurane anesthesia in 129 patients. Considering the high accuracy of this method, a new EEG monitoring system could be developed to assist the anesthesiologist in estimating the depth of anesthesia in a rapid and accurate manner.

  2. Entropy and Energy, - a Universal Competition

    NASA Astrophysics Data System (ADS)

    Müller, Ingo

    2008-12-01

    When a body approaches equilibrium, energy tends to a minimum and entropy tends to a maximum. Often, or usually, the two tendencies favour different configurations of the body. Thus energy is deterministic in the sense that it favours fixed positions for the atoms, while entropy randomizes the positions. Both may exert considerable forces in the attempt to reach their objectives. Therefore they have to compromise; indeed, under most circumstances it is the available free energy which achieves a minimum. For low temperatures that free energy is energy itself, while for high temperatures it is determined by entropy. Several examples are provided for the roles of energy and entropy as competitors: - Planetary atmospheres; - osmosis; - phase transitions in gases and liquids and in shape memory alloys, and - chemical reactions, viz. the Haber Bosch synthesis of ammonia and photosynthesis. Some historical remarks are strewn through the text to make the reader appreciate the difficulties encountered by the pioneers in understanding the subtlety of the concept of entropy, and in convincing others of the validity and relevance of their arguments.

  3. Enzyme catalysis by entropy without Circe effect

    PubMed Central

    Kazemi, Masoud; Himo, Fahmi; Åqvist, Johan

    2016-01-01

    Entropic effects have often been invoked to explain the extraordinary catalytic power of enzymes. In particular, the hypothesis that enzymes can use part of the substrate-binding free energy to reduce the entropic penalty associated with the subsequent chemical transformation has been very influential. The enzymatic reaction of cytidine deaminase appears to be a distinct example. Here, substrate binding is associated with a significant entropy loss that closely matches the activation entropy penalty for the uncatalyzed reaction in water, whereas the activation entropy for the rate-limiting catalytic step in the enzyme is close to zero. Herein, we report extensive computer simulations of the cytidine deaminase reaction and its temperature dependence. The energetics of the catalytic reaction is first evaluated by density functional theory calculations. These results are then used to parametrize an empirical valence bond description of the reaction, which allows efficient sampling by molecular dynamics simulations and computation of Arrhenius plots. The thermodynamic activation parameters calculated by this approach are in excellent agreement with experimental data and indeed show an activation entropy close to zero for the rate-limiting transition state. However, the origin of this effect is a change of reaction mechanism compared the uncatalyzed reaction. The enzyme operates by hydroxide ion attack, which is intrinsically associated with a favorable activation entropy. Hence, this has little to do with utilization of binding free energy to pay the entropic penalty but rather reflects how a preorganized active site can stabilize a reaction path that is not operational in solution. PMID:26755610

  4. Enzyme catalysis by entropy without Circe effect.

    PubMed

    Kazemi, Masoud; Himo, Fahmi; Åqvist, Johan

    2016-03-01

    Entropic effects have often been invoked to explain the extraordinary catalytic power of enzymes. In particular, the hypothesis that enzymes can use part of the substrate-binding free energy to reduce the entropic penalty associated with the subsequent chemical transformation has been very influential. The enzymatic reaction of cytidine deaminase appears to be a distinct example. Here, substrate binding is associated with a significant entropy loss that closely matches the activation entropy penalty for the uncatalyzed reaction in water, whereas the activation entropy for the rate-limiting catalytic step in the enzyme is close to zero. Herein, we report extensive computer simulations of the cytidine deaminase reaction and its temperature dependence. The energetics of the catalytic reaction is first evaluated by density functional theory calculations. These results are then used to parametrize an empirical valence bond description of the reaction, which allows efficient sampling by molecular dynamics simulations and computation of Arrhenius plots. The thermodynamic activation parameters calculated by this approach are in excellent agreement with experimental data and indeed show an activation entropy close to zero for the rate-limiting transition state. However, the origin of this effect is a change of reaction mechanism compared the uncatalyzed reaction. The enzyme operates by hydroxide ion attack, which is intrinsically associated with a favorable activation entropy. Hence, this has little to do with utilization of binding free energy to pay the entropic penalty but rather reflects how a preorganized active site can stabilize a reaction path that is not operational in solution.

  5. Approximate von Neumann entropy for directed graphs.

    PubMed

    Ye, Cheng; Wilson, Richard C; Comin, César H; Costa, Luciano da F; Hancock, Edwin R

    2014-05-01

    In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks.

  6. Valence bond and von Neumann entanglement entropy in Heisenberg ladders.

    PubMed

    Kallin, Ann B; González, Iván; Hastings, Matthew B; Melko, Roger G

    2009-09-11

    We present a direct comparison of the recently proposed valence bond entanglement entropy and the von Neumann entanglement entropy on spin-1/2 Heisenberg systems using quantum Monte Carlo and density-matrix renormalization group simulations. For one-dimensional chains we show that the valence bond entropy can be either less or greater than the von Neumann entropy; hence, it cannot provide a bound on the latter. On ladder geometries, simulations with up to seven legs are sufficient to indicate that the von Neumann entropy in two dimensions obeys an area law, even though the valence bond entanglement entropy has a multiplicative logarithmic correction.

  7. Measuring entanglement entropies in many-body systems

    SciTech Connect

    Klich, Israel; Refael, Gil; Silva, Alessandro

    2006-09-15

    We explore the relation between entanglement entropy of quantum many-body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that, in general, the Shannon entropy of the probability distribution of certain symmetry observables gives a lower bound to the entropy. In some cases this bound is saturated and directly gives the entropy. We also show other cases in which the probability distribution contains enough information to extract the entropy: we show how this is done in several examples including BEC wave functions, the Dicke model, XY spin chain, and chains with strong randomness.

  8. Input Type and Parameter Resetting: Is Naturalistic Input Necessary?

    ERIC Educational Resources Information Center

    Rothman, Jason; Iverson, Michael

    2007-01-01

    It has been argued that extended exposure to naturalistic input provides L2 learners with more of an opportunity to converge of target morphosyntactic competence as compared to classroom-only environments, given that the former provide more positive evidence of less salient linguistic properties than the latter (e.g., Isabelli 2004). Implicitly,…

  9. Content-based retrieval of medical images with relative entropy

    NASA Astrophysics Data System (ADS)

    Moshfeghi, Mehran; Saiz, Craig; Yu, Hua

    2004-04-01

    Medical image databases are growing at a rapid rate because of the increase in digital medical imaging modalities and the deployment of Picture Archiving and Communication Systems (PACS), Electronic Medical Records (EMR) and telemedicine applications. There is growing research interest in Content-Based Image Retrieval (CBIR) of medical images from such digital archives. A new distance function for CBIR is presented for measuring the similarity between two images. The distance function is a variant of relative entropy, or the Kullback-Liebler distance. The new distance is the sum of the relative entropy of the two images to each other. The latter is a symmetric non-negative function and is only zero when the two images have identical probability distributions. This method has been implemented in a prototype system and has been applied to a database of medical images. Initial results demonstrate improvements over L1-norm and L2-norm histogram matching. The method is computationally simple since it does not require image segmentation. It is invariant to translation, rotation and scaling. The method has also been extended to support retrieval based on Region-Of-Interest (ROI) queries.

  10. Mass exchange processes with input

    NASA Astrophysics Data System (ADS)

    Krapivsky, P. L.

    2015-05-01

    We investigate a system of interacting clusters evolving through mass exchange and supplemented by input of small clusters. Three possibilities depending on the rate of exchange generically occur when input is homogeneous: continuous growth, gelation, and instantaneous gelation. We mostly study the growth regime using scaling methods. An exchange process with reaction rates equal to the product of reactant masses admits an exact solution which allows us to justify the validity of scaling approaches in this special case. We also investigate exchange processes with a localized input. We show that if the diffusion coefficients are mass-independent, the cluster mass distribution becomes stationary and develops an algebraic tail far away from the source.

  11. Bayesian cross-entropy methodology for optimal design of validation experiments

    NASA Astrophysics Data System (ADS)

    Jiang, X.; Mahadevan, S.

    2006-07-01

    An important concern in the design of validation experiments is how to incorporate the mathematical model in the design in order to allow conclusive comparisons of model prediction with experimental output in model assessment. The classical experimental design methods are more suitable for phenomena discovery and may result in a subjective, expensive, time-consuming and ineffective design that may adversely impact these comparisons. In this paper, an integrated Bayesian cross-entropy methodology is proposed to perform the optimal design of validation experiments incorporating the computational model. The expected cross entropy, an information-theoretic distance between the distributions of model prediction and experimental observation, is defined as a utility function to measure the similarity of two distributions. A simulated annealing algorithm is used to find optimal values of input variables through minimizing or maximizing the expected cross entropy. The measured data after testing with the optimum input values are used to update the distribution of the experimental output using Bayes theorem. The procedure is repeated to adaptively design the required number of experiments for model assessment, each time ensuring that the experiment provides effective comparison for validation. The methodology is illustrated for the optimal design of validation experiments for a three-leg bolted joint structure and a composite helicopter rotor hub component.

  12. An Entropy Model for Artificial Grammar Learning

    PubMed Central

    Pothos, Emmanuel M.

    2010-01-01

    A model is proposed to characterize the type of knowledge acquired in artificial grammar learning (AGL). In particular, Shannon entropy is employed to compute the complexity of different test items in an AGL task, relative to the training items. According to this model, the more predictable a test item is from the training items, the more likely it is that this item should be selected as compatible with the training items. The predictions of the entropy model are explored in relation to the results from several previous AGL datasets and compared to other AGL measures. This particular approach in AGL resonates well with similar models in categorization and reasoning which also postulate that cognitive processing is geared towards the reduction of entropy. PMID:21607072

  13. Entropy production of doubly stochastic quantum channels

    NASA Astrophysics Data System (ADS)

    Müller-Hermes, Alexander; Stilck França, Daniel; Wolf, Michael M.

    2016-02-01

    We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.

  14. Zipf's law, power laws and maximum entropy

    NASA Astrophysics Data System (ADS)

    Visser, Matt

    2013-04-01

    Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines—from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation (RGF) attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present paper I argue that the specific cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified.

  15. Adjusting protein graphs based on graph entropy.

    PubMed

    Peng, Sheng-Lung; Tsay, Yu-Wei

    2014-01-01

    Measuring protein structural similarity attempts to establish a relationship of equivalence between polymer structures based on their conformations. In several recent studies, researchers have explored protein-graph remodeling, instead of looking a minimum superimposition for pairwise proteins. When graphs are used to represent structured objects, the problem of measuring object similarity become one of computing the similarity between graphs. Graph theory provides an alternative perspective as well as efficiency. Once a protein graph has been created, its structural stability must be verified. Therefore, a criterion is needed to determine if a protein graph can be used for structural comparison. In this paper, we propose a measurement for protein graph remodeling based on graph entropy. We extend the concept of graph entropy to determine whether a graph is suitable for representing a protein. The experimental results suggest that when applied, graph entropy helps a conformational on protein graph modeling. Furthermore, it indirectly contributes to protein structural comparison if a protein graph is solid.

  16. Horizon Entropy from Quantum Gravity Condensates.

    PubMed

    Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo

    2016-05-27

    We construct condensate states encoding the continuum spherically symmetric quantum geometry of a horizon in full quantum gravity, i.e., without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits a holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein-Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one.

  17. Generalized gravitational entropy without replica symmetry

    NASA Astrophysics Data System (ADS)

    Camps, Joan; Kelly, William R.

    2015-03-01

    We explore several extensions of the generalized entropy construction of Lewkowycz and Maldacena, including a formulation that does not rely on preserving replica symmetry in the bulk. We show that an appropriately general ansatz for the analytically continued replica metric gives us the flexibility needed to solve the gravitational field equations beyond general relativity. As an application of this observation we study EinsteinGauss-Bonnet gravity with a small Gauss-Bonnet coupling and derive the condition that the holographic entanglement entropy must be evaluated on a surface which extremizes the Jacobson-Myers entropy. We find that in both general relativity and Einstein-Gauss-Bonnet gravity replica symmetry breaking terms are permitted by the field equations, suggesting that they do not generically vanish.

  18. Holographic entanglement entropy of surface defects

    NASA Astrophysics Data System (ADS)

    Gentle, Simon A.; Gutperle, Michael; Marasinou, Chrysostomos

    2016-04-01

    We calculate the holographic entanglement entropy in type IIB supergravity solutions that are dual to half-BPS disorder-type surface defects in N=4 supersymmetric Yang-Mills theory. The entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. Using the bubbling supergravity solutions we also compute the expectation value of the defect operator. Combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of Lewkowycz and Maldacena [1] to obtain a second expression for the entanglement entropy. Our two expressions agree up to an additional term, whose possible origin and significance is discussed.

  19. Entropy production of doubly stochastic quantum channels

    SciTech Connect

    Müller-Hermes, Alexander; Stilck França, Daniel Wolf, Michael M.

    2016-02-15

    We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.

  20. Transfer Entropy and Transient Limits of Computation

    PubMed Central

    Prokopenko, Mikhail; Lizier, Joseph T.

    2014-01-01

    Transfer entropy is a recently introduced information-theoretic measure quantifying directed statistical coherence between spatiotemporal processes, and is widely used in diverse fields ranging from finance to neuroscience. However, its relationships to fundamental limits of computation, such as Landauer's limit, remain unknown. Here we show that in order to increase transfer entropy (predictability) by one bit, heat flow must match or exceed Landauer's limit. Importantly, we generalise Landauer's limit to bi-directional information dynamics for non-equilibrium processes, revealing that the limit applies to prediction, in addition to retrodiction (information erasure). Furthermore, the results are related to negentropy, and to Bremermann's limit and the Bekenstein bound, producing, perhaps surprisingly, lower bounds on the computational deceleration and information loss incurred during an increase in predictability about the process. The identified relationships set new computational limits in terms of fundamental physical quantities, and establish transfer entropy as a central measure connecting information theory, thermodynamics and theory of computation. PMID:24953547

  1. Entropy Generation and Human Aging: Lifespan Entropy and Effect of Physical Activity Level

    NASA Astrophysics Data System (ADS)

    Silva, Carlos; Annamalai, Kalyan

    2008-06-01

    The first and second laws of thermodynamics were applied to biochemical reactions typical of human metabolism. An open-system model was used for a human body. Energy conservation, availability and entropy balances were performed to obtain the entropy generated for the main food components. Quantitative results for entropy generation were obtained as a function of age using the databases from the U.S. Food and Nutrition Board (FNB) and Centers for Disease Control and Prevention (CDC), which provide energy requirements and food intake composition as a function of age, weight and stature. Numerical integration was performed through human lifespan for different levels of physical activity. Results were presented and analyzed. Entropy generated over the lifespan of average individuals (natural death) was found to be 11,404 kJ/ºK per kg of body mass with a rate of generation three times higher on infants than on the elderly. The entropy generated predicts a life span of 73.78 and 81.61 years for the average U.S. male and female individuals respectively, which are values that closely match the average lifespan from statistics (74.63 and 80.36 years). From the analysis of the effect of different activity levels, it is shown that entropy generated increases with physical activity, suggesting that exercise should be kept to a “healthy minimum” if entropy generation is to be minimized.

  2. Autonomous entropy-based intelligent experimental design

    NASA Astrophysics Data System (ADS)

    Malakar, Nabin Kumar

    2011-07-01

    The aim of this thesis is to explore the application of probability and information theory in experimental design, and to do so in a way that combines what we know about inference and inquiry in a comprehensive and consistent manner. Present day scientific frontiers involve data collection at an ever-increasing rate. This requires that we find a way to collect the most relevant data in an automated fashion. By following the logic of the scientific method, we couple an inference engine with an inquiry engine to automate the iterative process of scientific learning. The inference engine involves Bayesian machine learning techniques to estimate model parameters based upon both prior information and previously collected data, while the inquiry engine implements data-driven exploration. By choosing an experiment whose distribution of expected results has the maximum entropy, the inquiry engine selects the experiment that maximizes the expected information gain. The coupled inference and inquiry engines constitute an autonomous learning method for scientific exploration. We apply it to a robotic arm to demonstrate the efficacy of the method. Optimizing inquiry involves searching for an experiment that promises, on average, to be maximally informative. If the set of potential experiments is described by many parameters, the search involves a high-dimensional entropy space. In such cases, a brute force search method will be slow and computationally expensive. We develop an entropy-based search algorithm, called nested entropy sampling, to select the most informative experiment. This helps to reduce the number of computations necessary to find the optimal experiment. We also extended the method of maximizing entropy, and developed a method of maximizing joint entropy so that it could be used as a principle of collaboration between two robots. This is a major achievement of this thesis, as it allows the information-based collaboration between two robotic units towards a same

  3. Entropy Inequality Violations from Ultraspinning Black Holes.

    PubMed

    Hennigar, Robie A; Mann, Robert B; Kubizňák, David

    2015-07-17

    We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold.

  4. Entanglement entropy of subtracted geometry black holes

    NASA Astrophysics Data System (ADS)

    Cvetič, Mirjam; Saleem, Zain H.; Satz, Alejandro

    2014-09-01

    We compute the entanglement entropy of minimally coupled scalar fields on subtracted geometry black hole backgrounds, focusing on the logarithmic corrections. We notice that matching between the entanglement entropy of original black holes and their subtracted counterparts is only at the order of the area term. The logarithmic correction term is not only different but also, in general, changes sign in the subtracted case. We apply Harrison transformations to the original black holes and find out the choice of the Harrison parameters for which the logarithmic corrections vanish.

  5. Maximum entropy spherical deconvolution for diffusion MRI.

    PubMed

    Alexander, Daniel C

    2005-01-01

    This paper proposes a maximum entropy method for spherical deconvolution. Spherical deconvolution arises in various inverse problems. This paper uses the method to reconstruct the distribution of microstructural fibre orientations from diffusion MRI measurements. Analysis shows that the PASMRI algorithm, one of the most accurate diffusion MRI reconstruction algorithms in the literature, is a special case of the maximum entropy spherical deconvolution. Experiments compare the new method to linear spherical deconvolution, used previously in diffusion MRI, and to the PASMRI algorithm. The new method compares favourably both in simulation and on standard brain-scan data.

  6. Wehrl entropy, Lieb conjecture, and entanglement monotones

    SciTech Connect

    Mintert, Florian; Zyczkowski, Karol

    2004-02-01

    We propose to quantify the entanglement of pure states of NxN bipartite quantum systems by defining its Husimi distribution with respect to SU(N)xSU(N) coherent states. The Wehrl entropy is minimal if and only if the analyzed pure state is separable. The excess of the Wehrl entropy is shown to be equal to the subentropy of the mixed state obtained by partial trace of the bipartite pure state. This quantity, as well as the generalized (Renyi) subentropies, are proved to be Schur concave, so they are entanglement monotones and may be used as alternative measures of entanglement.

  7. Black hole entropy without brick walls

    NASA Astrophysics Data System (ADS)

    Xiang, Li

    2002-07-01

    The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of a Schwarzschild black hole. When the new equation of state density is utilized to investigate the entropy of a scalar field outside the horizon of a static black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.

  8. High resolution schemes and the entropy condition

    NASA Technical Reports Server (NTRS)

    Osher, S.; Chakravarthy, S.

    1983-01-01

    A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five point band width, approximations to scalar conservation laws, is presented. These schemes are constructed to also satisfy a single discrete entropy inequality. Thus, in the convex flux case, convergence is proven to be the unique physically correct solution. For hyperbolic systems of conservation laws, this construction is used formally to extend the first author's first order accurate scheme, and show (under some minor technical hypotheses) that limit solutions satisfy an entropy inequality. Results concerning discrete shocks, a maximum principle, and maximal order of accuracy are obtained. Numerical applications are also presented.

  9. Distribution entropy analysis of epileptic EEG signals.

    PubMed

    Li, Peng; Yan, Chang; Karmakar, Chandan; Liu, Changchun

    2015-01-01

    It is an open-ended challenge to accurately detect the epileptic seizures through electroencephalogram (EEG) signals. Recently published studies have made elaborate attempts to distinguish between the normal and epileptic EEG signals by advanced nonlinear entropy methods, such as the approximate entropy, sample entropy, fuzzy entropy, and permutation entropy, etc. Most recently, a novel distribution entropy (DistEn) has been reported to have superior performance compared with the conventional entropy methods for especially short length data. We thus aimed, in the present study, to show the potential of DistEn in the analysis of epileptic EEG signals. The publicly-accessible Bonn database which consisted of normal, interictal, and ictal EEG signals was used in this study. Three different measurement protocols were set for better understanding the performance of DistEn, which are: i) calculate the DistEn of a specific EEG signal using the full recording; ii) calculate the DistEn by averaging the results for all its possible non-overlapped 5 second segments; and iii) calculate it by averaging the DistEn values for all the possible non-overlapped segments of 1 second length, respectively. Results for all three protocols indicated a statistically significantly increased DistEn for the ictal class compared with both the normal and interictal classes. Besides, the results obtained under the third protocol, which only used very short segments (1 s) of EEG recordings showed a significantly (p <; 0.05) increased DistEn for the interictal class in compassion with the normal class, whereas both analyses using relatively long EEG signals failed in tracking this difference between them, which may be due to a nonstationarity effect on entropy algorithm. The capability of discriminating between the normal and interictal EEG signals is of great clinical relevance since it may provide helpful tools for the detection of a seizure onset. Therefore, our study suggests that the Dist

  10. Refractory High-Entropy Alloys (Postprint)

    DTIC Science & Technology

    2010-06-23

    AFRL-RX-WP-JA-2015-0119 REFRACTORY HIGH-ENTROPY ALLOYS (POSTPRINT) D.B. Miracle AFRL/RXCM O.N. Senkov UES, Inc. G.B. Wilks...AUTHOR(S) D.B. Miracle - AFRL/RXCM O.N. Senkov - UES, Inc. G.B. Wilks - General Dynamics, Corp. C.P. Chuang and P.K. Liaw - The University...intermetRefractory high-entropy alloys O.N. Senkov a,b,*, G.B. Wilks a,c, D.B. Miracle a, C.P. Chuang d, P.K. Liawd aAir Force Research Laboratory

  11. Analog Input Data Acquisition Software

    NASA Technical Reports Server (NTRS)

    Arens, Ellen

    2009-01-01

    DAQ Master Software allows users to easily set up a system to monitor up to five analog input channels and save the data after acquisition. This program was written in LabVIEW 8.0, and requires the LabVIEW runtime engine 8.0 to run the executable.

  12. Optimal Inputs for System Identification.

    DTIC Science & Technology

    1995-09-01

    The derivation of the power spectral density of the optimal input for system identification is addressed in this research. Optimality is defined in...identification potential of general System Identification algorithms, a new and efficient System Identification algorithm that employs Iterated Weighted Least

  13. World Input-Output Network

    PubMed Central

    Cerina, Federica; Zhu, Zhen; Chessa, Alessandro; Riccaboni, Massimo

    2015-01-01

    Production systems, traditionally analyzed as almost independent national systems, are increasingly connected on a global scale. Only recently becoming available, the World Input-Output Database (WIOD) is one of the first efforts to construct the global multi-regional input-output (GMRIO) tables. By viewing the world input-output system as an interdependent network where the nodes are the individual industries in different economies and the edges are the monetary goods flows between industries, we analyze respectively the global, regional, and local network properties of the so-called world input-output network (WION) and document its evolution over time. At global level, we find that the industries are highly but asymmetrically connected, which implies that micro shocks can lead to macro fluctuations. At regional level, we find that the world production is still operated nationally or at most regionally as the communities detected are either individual economies or geographically well defined regions. Finally, at local level, for each industry we compare the network-based measures with the traditional methods of backward linkages. We find that the network-based measures such as PageRank centrality and community coreness measure can give valuable insights into identifying the key industries. PMID:26222389

  14. The advanced LIGO input optics

    NASA Astrophysics Data System (ADS)

    Mueller, Chris L.; Arain, Muzammil A.; Ciani, Giacomo; DeRosa, Ryan. T.; Effler, Anamaria; Feldbaum, David; Frolov, Valery V.; Fulda, Paul; Gleason, Joseph; Heintze, Matthew; Kawabe, Keita; King, Eleanor J.; Kokeyama, Keiko; Korth, William Z.; Martin, Rodica M.; Mullavey, Adam; Peold, Jan; Quetschke, Volker; Reitze, David H.; Tanner, David B.; Vorvick, Cheryl; Williams, Luke F.; Mueller, Guido

    2016-01-01

    The advanced LIGO gravitational wave detectors are nearing their design sensitivity and should begin taking meaningful astrophysical data in the fall of 2015. These resonant optical interferometers will have unprecedented sensitivity to the strains caused by passing gravitational waves. The input optics play a significant part in allowing these devices to reach such sensitivities. Residing between the pre-stabilized laser and the main interferometer, the input optics subsystem is tasked with preparing the laser beam for interferometry at the sub-attometer level while operating at continuous wave input power levels ranging from 100 mW to 150 W. These extreme operating conditions required every major component to be custom designed. These designs draw heavily on the experience and understanding gained during the operation of Initial LIGO and Enhanced LIGO. In this article, we report on how the components of the input optics were designed to meet their stringent requirements and present measurements showing how well they have lived up to their design.

  15. Lab Inputs for Common Micros.

    ERIC Educational Resources Information Center

    Tinker, Robert

    1984-01-01

    The game paddle inputs of Apple microcomputers provide a simple way to get laboratory measurements into the computer. Discusses these game paddles and the necessary interface software. Includes schematics for Apple built-in paddle electronics, TRS-80 game paddle I/O, Commodore circuit for user port, and bus interface for Sinclair/Timex, Commodore,…

  16. The advanced LIGO input optics

    SciTech Connect

    Mueller, Chris L. Arain, Muzammil A.; Ciani, Giacomo; Feldbaum, David; Fulda, Paul; Gleason, Joseph; Heintze, Matthew; Martin, Rodica M.; Reitze, David H.; Tanner, David B.; Williams, Luke F.; Mueller, Guido; DeRosa, Ryan T.; Effler, Anamaria; Kokeyama, Keiko; Frolov, Valery V.; Mullavey, Adam; Kawabe, Keita; Vorvick, Cheryl; King, Eleanor J.; and others

    2016-01-15

    The advanced LIGO gravitational wave detectors are nearing their design sensitivity and should begin taking meaningful astrophysical data in the fall of 2015. These resonant optical interferometers will have unprecedented sensitivity to the strains caused by passing gravitational waves. The input optics play a significant part in allowing these devices to reach such sensitivities. Residing between the pre-stabilized laser and the main interferometer, the input optics subsystem is tasked with preparing the laser beam for interferometry at the sub-attometer level while operating at continuous wave input power levels ranging from 100 mW to 150 W. These extreme operating conditions required every major component to be custom designed. These designs draw heavily on the experience and understanding gained during the operation of Initial LIGO and Enhanced LIGO. In this article, we report on how the components of the input optics were designed to meet their stringent requirements and present measurements showing how well they have lived up to their design.

  17. Signal Prediction With Input Identification

    NASA Technical Reports Server (NTRS)

    Juang, Jer-Nan; Chen, Ya-Chin

    1999-01-01

    A novel coding technique is presented for signal prediction with applications including speech coding, system identification, and estimation of input excitation. The approach is based on the blind equalization method for speech signal processing in conjunction with the geometric subspace projection theory to formulate the basic prediction equation. The speech-coding problem is often divided into two parts, a linear prediction model and excitation input. The parameter coefficients of the linear predictor and the input excitation are solved simultaneously and recursively by a conventional recursive least-squares algorithm. The excitation input is computed by coding all possible outcomes into a binary codebook. The coefficients of the linear predictor and excitation, and the index of the codebook can then be used to represent the signal. In addition, a variable-frame concept is proposed to block the same excitation signal in sequence in order to reduce the storage size and increase the transmission rate. The results of this work can be easily extended to the problem of disturbance identification. The basic principles are outlined in this report and differences from other existing methods are discussed. Simulations are included to demonstrate the proposed method.

  18. Entropy analysis in foreign exchange markets and economic crisis

    NASA Astrophysics Data System (ADS)

    Ha, Jin-Gi; Yim, Kyubin; Kim, Seunghwan; Jung, Woo-Sung

    2012-08-01

    We investigate the relative market efficiency in 11 foreign exchange markets by using the Lempel-Ziv (LZ) complexity algorithm and several entropy values such as the Shannon entropy, the approximate entropy, and the sample entropy. With daily data in 11 foreign exchange markets from Jan. 2000 to Sep. 2011, we observe that mature markets have higher LZ complexities and entropy values than emerging markets. Furthermore, with sliding time windows, we also investigate the temporal evolutions of those entropies from Jan. 1994 to Sep. 2011, and we find that, after an economic crisis, the approximate entropy and the sample entropy of mature markets such as Japan, Europe and the United Kingdom suddenly become lower.

  19. Gravitational correlation, black hole entropy, and information conservation

    NASA Astrophysics Data System (ADS)

    He, DongShan; Cai, QingYu

    2017-04-01

    When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by Verlinde's paper, we first calculate the entropy change of a system when gravity does positive work on this system. Based on the concept of gravitational correlation entropy, we prove that the entropy of a Schwarzschild black hole originates from the gravitational correlations between the interior matters of the black hole. By analyzing the gravitational correlation entropies in the process of Hawking radiation in a general context, we prove that the reduced entropy of a black hole is exactly carried away by the radiation and the gravitational correlations between these radiating particles, and the entropy or information is conserved at all times during Hawking radiation. Finally, we attempt to give a unified description of the non-extensive black-hole entropy and the extensive entropy of ordinary matter.

  20. A Study of Turkish Chemistry Undergraduates' Understandings of Entropy

    ERIC Educational Resources Information Center

    Sozbilir, Mustafa; Bennett, Judith M.

    2007-01-01

    Entropy is that fundamental concept of chemical thermodynamics, which explains the natural tendency of matter and energy in the Universe. The analysis presents the description of entropy, as understood by the Turkish chemistry undergraduates.

  1. Gacs quantum algorithmic entropy in infinite dimensional Hilbert spaces

    SciTech Connect

    Benatti, Fabio; Oskouei, Samad Khabbazi Deh Abad, Ahmad Shafiei

    2014-08-15

    We extend the notion of Gacs quantum algorithmic entropy, originally formulated for finitely many qubits, to infinite dimensional quantum spin chains and investigate the relation of this extension with two quantum dynamical entropies that have been proposed in recent years.

  2. A logarithmic correction in the entropy functional formalism

    NASA Astrophysics Data System (ADS)

    Hammad, Fayçal; Faizal, Mir

    2016-04-01

    The entropy functional formalism allows one to recover general relativity, modified gravity theories, as well as the Bekenstein-Hawking entropy formula. In most approaches to quantum gravity, the Bekenstein-Hawking’s entropy formula acquires a logarithmic correction term. As such terms occur almost universally in most approaches to quantum gravity, we analyze the effect of such terms on the entropy functional formalism. We demonstrate that the leading correction to the micro-canonical entropy in the entropy functional formalism can be used to recover modified theories of gravity already obtained with an uncorrected micro-canonical entropy. Furthermore, since the entropy functional formalism reproduces modified gravity, the rise of gravity-dependent logarithmic corrections turns out to be one way to impose constraints on these theories of modified gravity. The constraints found here for the simple case of an ℱ(R)-gravity are the same as those obtained in the literature from cosmological considerations.

  3. Three chamber negative ion source

    DOEpatents

    Leung, Ka-Ngo; Ehlers, Kenneth W.; Hiskes, John R.

    1985-01-01

    A negative ion vessel is divided into an excitation chamber, a negative ionization chamber and an extraction chamber by two magnetic filters. Input means introduces neutral molecules into a first chamber where a first electron discharge means vibrationally excites the molecules which migrate to a second chamber. In the second chamber a second electron discharge means ionizes the molecules, producing negative ions which are extracted into or by a third chamber. A first magnetic filter prevents high energy electrons from entering the negative ionization chamber from the excitation chamber. A second magnetic filter prevents high energy electrons from entering the extraction chamber from the negative ionizing chamber. An extraction grid at the end of the negative ion vessel attracts negative ions into the third chamber and accelerates them. Another grid, located adjacent to the extraction grid, carries a small positive voltage in order to inhibit positive ions from migrating into the extraction chamber and contour the plasma potential. Additional electrons can be suppressed from the output flux using ExB forces provided by magnetic field means and the extractor grid electric potential.

  4. Volcano shapes, entropies, and eruption probabilities

    NASA Astrophysics Data System (ADS)

    Gudmundsson, Agust; Mohajeri, Nahid

    2014-05-01

    We propose that the shapes of polygenetic volcanic edifices reflect the shapes of the associated probability distributions of eruptions. In this view, the peak of a given volcanic edifice coincides roughly with the peak of the probability (or frequency) distribution of its eruptions. The broadness and slopes of the edifices vary widely, however. The shapes of volcanic edifices can be approximated by various distributions, either discrete (binning or histogram approximation) or continuous. For a volcano shape (profile) approximated by a normal curve, for example, the broadness would be reflected in its standard deviation (spread). Entropy (S) of a discrete probability distribution is a measure of the absolute uncertainty as to the next outcome/message: in this case, the uncertainty as to time and place of the next eruption. A uniform discrete distribution (all bins of equal height), representing a flat volcanic field or zone, has the largest entropy or uncertainty. For continuous distributions, we use differential entropy, which is a measure of relative uncertainty, or uncertainty change, rather than absolute uncertainty. Volcano shapes can be approximated by various distributions, from which the entropies and thus the uncertainties as regards future eruptions can be calculated. We use the Gibbs-Shannon formula for the discrete entropies and the analogues general formula for the differential entropies and compare their usefulness for assessing the probabilities of eruptions in volcanoes. We relate the entropies to the work done by the volcano during an eruption using the Helmholtz free energy. Many factors other than the frequency of eruptions determine the shape of a volcano. These include erosion, landslides, and the properties of the erupted materials (including their angle of repose). The exact functional relation between the volcano shape and the eruption probability distribution must be explored for individual volcanoes but, once established, can be used to

  5. Sparse kernel entropy component analysis for dimensionality reduction of neuroimaging data.

    PubMed

    Jiang, Qikun; Shi, Jun

    2014-01-01

    The neuroimaging data typically has extremely high dimensions. Therefore, dimensionality reduction is commonly used to extract discriminative features. Kernel entropy component analysis (KECA) is a newly developed data transformation method, where the key idea is to preserve the most estimated Renyi entropy of the input space data set via a kernel-based estimator. Despite its good performance, KECA still suffers from the problem of low computational efficiency for large-scale data. In this paper, we proposed a sparse KECA (SKECA) algorithm with the recursive divide-and-conquer based solution, and then applied it to perform dimensionality reduction of neuroimaging data for classification of the Alzheimer's disease (AD). We compared the SKECA with KECA, principal component analysis (PCA), kernel PCA (KPCA) and sparse KPCA. The experimental results indicate that the proposed SKECA has most superior performance to all other algorithms when extracting discriminative features from neuroimaging data for AD classification.

  6. Systems and methods for reconfiguring input devices

    NASA Technical Reports Server (NTRS)

    Lancaster, Jeff (Inventor); De Mers, Robert E. (Inventor)

    2012-01-01

    A system includes an input device having first and second input members configured to be activated by a user. The input device is configured to generate activation signals associated with activation of the first and second input members, and each of the first and second input members are associated with an input function. A processor is coupled to the input device and configured to receive the activation signals. A memory coupled to the processor, and includes a reconfiguration module configured to store the input functions assigned to the first and second input members and, upon execution of the processor, to reconfigure the input functions assigned to the input members when the first input member is inoperable.

  7. Waste heat boiler optimization by entropy minimization principle

    SciTech Connect

    Reddy, B.V.; Murali, J.; Satheesh, V.S.; Nag, P.K.

    1996-12-31

    A second law analysis has been undertaken for a waste heat boiler having an economizer, evaporator and superheater. Following the principle of minimization of entropy generation, a general equation for entropy generation number is derived, which incorporates all the operating variables. By differentiating the entropy generation number equation with respect to the operating parameters, various optimization parameters can be obtained. Few illustrations have been made to see the effect of various parameters on entropy generation number.

  8. Maximum entropy, word-frequency, Chinese characters, and multiple meanings.

    PubMed

    Yan, Xiaoyong; Minnhagen, Petter

    2015-01-01

    The word-frequency distribution of a text written by an author is well accounted for by a maximum entropy distribution, the RGF (random group formation)-prediction. The RGF-distribution is completely determined by the a priori values of the total number of words in the text (M), the number of distinct words (N) and the number of repetitions of the most common word (k(max)). It is here shown that this maximum entropy prediction also describes a text written in Chinese characters. In particular it is shown that although the same Chinese text written in words and Chinese characters have quite differently shaped distributions, they are nevertheless both well predicted by their respective three a priori characteristic values. It is pointed out that this is analogous to the change in the shape of the distribution when translating a given text to another language. Another consequence of the RGF-prediction is that taking a part of a long text will change the input parameters (M, N, k(max)) and consequently also the shape of the frequency distribution. This is explicitly confirmed for texts written in Chinese characters. Since the RGF-prediction has no system-specific information beyond the three a priori values (M, N, k(max)), any specific language characteristic has to be sought in systematic deviations from the RGF-prediction and the measured frequencies. One such systematic deviation is identified and, through a statistical information theoretical argument and an extended RGF-model, it is proposed that this deviation is caused by multiple meanings of Chinese characters. The effect is stronger for Chinese characters than for Chinese words. The relation between Zipf's law, the Simon-model for texts and the present results are discussed.

  9. Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings

    PubMed Central

    Yan, Xiaoyong; Minnhagen, Petter

    2015-01-01

    The word-frequency distribution of a text written by an author is well accounted for by a maximum entropy distribution, the RGF (random group formation)-prediction. The RGF-distribution is completely determined by the a priori values of the total number of words in the text (M), the number of distinct words (N) and the number of repetitions of the most common word (kmax). It is here shown that this maximum entropy prediction also describes a text written in Chinese characters. In particular it is shown that although the same Chinese text written in words and Chinese characters have quite differently shaped distributions, they are nevertheless both well predicted by their respective three a priori characteristic values. It is pointed out that this is analogous to the change in the shape of the distribution when translating a given text to another language. Another consequence of the RGF-prediction is that taking a part of a long text will change the input parameters (M, N, kmax) and consequently also the shape of the frequency distribution. This is explicitly confirmed for texts written in Chinese characters. Since the RGF-prediction has no system-specific information beyond the three a priori values (M, N, kmax), any specific language characteristic has to be sought in systematic deviations from the RGF-prediction and the measured frequencies. One such systematic deviation is identified and, through a statistical information theoretical argument and an extended RGF-model, it is proposed that this deviation is caused by multiple meanings of Chinese characters. The effect is stronger for Chinese characters than for Chinese words. The relation between Zipf’s law, the Simon-model for texts and the present results are discussed. PMID:25955175

  10. Discovery and Entropy in the Revision of Technical Reports.

    ERIC Educational Resources Information Center

    Marder, Daniel

    A useful device in revising technical reports is the metaphor of entropy, which refers to the amount of disorder that is present in a system. Applied to communication theory, high entropy would correspond to increased amounts of unfamiliar or useless information in a text. Since entropy in rhetorical systems increases with the unfamiliarity of…

  11. LETTER TO THE EDITOR: Bias analysis in entropy estimation

    NASA Astrophysics Data System (ADS)

    Schürmann, Thomas

    2004-07-01

    We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulae of current entropy estimates recently discussed in the literature. The trade-off between bias reduction and the increase of the corresponding statistical error is analysed.

  12. Psychological Entropy: A Framework for Understanding Uncertainty-Related Anxiety

    ERIC Educational Resources Information Center

    Hirsh, Jacob B.; Mar, Raymond A.; Peterson, Jordan B.

    2012-01-01

    Entropy, a concept derived from thermodynamics and information theory, describes the amount of uncertainty and disorder within a system. Self-organizing systems engage in a continual dialogue with the environment and must adapt themselves to changing circumstances to keep internal entropy at a manageable level. We propose the entropy model of…

  13. Perceptual suppression revealed by adaptive multi-scale entropy analysis of local field potential in monkey visual cortex.

    PubMed

    Hu, Meng; Liang, Hualou

    2013-04-01

    Generalized flash suppression (GFS), in which a salient visual stimulus can be rendered invisible despite continuous retinal input, provides a rare opportunity to directly study the neural mechanism of visual perception. Previous work based on linear methods, such as spectral analysis, on local field potential (LFP) during GFS has shown that the LFP power at distinctive frequency bands are differentially modulated by perceptual suppression. Yet, the linear method alone may be insufficient for the full assessment of neural dynamic due to the fundamentally nonlinear nature of neural signals. In this study, we set forth to analyze the LFP data collected from multiple visual areas in V1, V2 and V4 of macaque monkeys while performing the GFS task using a nonlinear method - adaptive multi-scale entropy (AME) - to reveal the neural dynamic of perceptual suppression. In addition, we propose a new cross-entropy measure at multiple scales, namely adaptive multi-scale cross-entropy (AMCE), to assess the nonlinear functional connectivity between two cortical areas. We show that: (1) multi-scale entropy exhibits percept-related changes in all three areas, with higher entropy observed during perceptual suppression; (2) the magnitude of the perception-related entropy changes increases systematically over successive hierarchical stages (i.e. from lower areas V1 to V2, up to higher area V4); and (3) cross-entropy between any two cortical areas reveals higher degree of asynchrony or dissimilarity during perceptual suppression, indicating a decreased functional connectivity between cortical areas. These results, taken together, suggest that perceptual suppression is related to a reduced functional connectivity and increased uncertainty of neural responses, and the modulation of perceptual suppression is more effective at higher visual cortical areas. AME is demonstrated to be a useful technique in revealing the underlying dynamic of nonlinear/nonstationary neural signal.

  14. Entropy analysis of automatic sequences revisited: An entropy diagnostic for automaticity

    NASA Astrophysics Data System (ADS)

    Karamanos, Kostas

    2001-06-01

    We give a necessary entropy condition, valid for all automatic sequences read by lumping. We next establish new entropic decimation schemes for the Thue-Morse, the Rudin-Shapiro and the paperfolding sequences read by lumping.

  15. Information, entropy and fidelity in visual communication

    NASA Technical Reports Server (NTRS)

    Huck, Friedrich O.; Fales, Carl L.; Alter-Gartenberg, Rachel; Rahman, Zia-Ur

    1992-01-01

    This paper presents an assessment of visual communication that integrates the critical limiting factors of image gathering and display with the digital processing that is used to code and restore images. The approach focuses on two mathematical criteria, information and fidelity, and on their relationships to the entropy of the encoded data and to the visual quality of the restored image.

  16. Entropy conservation in simulations of magnetic reconnection

    SciTech Connect

    Birn, J.; Hesse, M.; Schindler, K.

    2006-09-15

    Entropy and mass conservation are investigated for the dynamic field evolution associated with fast magnetic reconnection, based on the 'Newton Challenge' problem [Birn et al., Geophys. Res. Lett. 32, L06105 (2005)]. In this problem, the formation of a thin current sheet and magnetic reconnection are initiated in a plane Harris-type current sheet by temporally limited, spatially varying, inflow of magnetic flux. Using resistive magnetohydrodynamic (MHD) and particle-in-cell (PIC) simulations, specifically the entropy and mass integrated along the magnetic flux tubes are compared between the simulations. In the MHD simulation these should be exactly conserved quantities, when slippage and Ohmic dissipation are negligible. It is shown that there is very good agreement between the conservation of these quantities in the two simulation approaches, despite the effects of dissipation, provided that the resistivity in the MHD simulation is strongly localized. This demonstrates that dissipation is highly localized in the PIC simulation also, and that heat flux across magnetic flux tubes has negligible effect as well, so that the entropy increase on a full flux tube remains small even during reconnection. The mass conservation also implies that the frozen-in flux condition of ideal MHD is a good integral approximation outside the reconnection site. This result lends support for using the entropy-conserving MHD approach not only before and after reconnection but even as a constraint connecting the two phases.

  17. Rényi entropy and conformal defects

    NASA Astrophysics Data System (ADS)

    Bianchi, Lorenzo; Meineri, Marco; Myers, Robert C.; Smolkin, Michael

    2016-07-01

    We propose a field theoretic framework for calculating the dependence of Rényi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Rényi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Rényi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.

  18. Entropy viscosity method applied to Euler equations

    SciTech Connect

    Delchini, M. O.; Ragusa, J. C.; Berry, R. A.

    2013-07-01

    The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)

  19. Nonextensive entropies derived from Gauss' principle

    NASA Astrophysics Data System (ADS)

    Wada, Tatsuaki

    2011-05-01

    Gauss' principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles.

  20. Le Chatelier's Principle, Temperature Effects, and Entropy.

    ERIC Educational Resources Information Center

    Campbell, J. Arthur

    1985-01-01

    One of the most useful methods of understanding chemical equilibria is provided by Le Chatelier's principle. The relationships between this principle, temperature, and entropy are discussed. Tables with thermodynamic data for some net reactions commonly used to illustrate the principle and for reactions involving gases are included. (JN)

  1. On the Entropy of Protein Families

    NASA Astrophysics Data System (ADS)

    Barton, John P.; Chakraborty, Arup K.; Cocco, Simona; Jacquin, Hugo; Monasson, Rémi

    2016-03-01

    Proteins are essential components of living systems, capable of performing a huge variety of tasks at the molecular level, such as recognition, signalling, copy, transport, ... The protein sequences realizing a given function may largely vary across organisms, giving rise to a protein family. Here, we estimate the entropy of those families based on different approaches, including Hidden Markov Models used for protein databases and inferred statistical models reproducing the low-order (1- and 2-point) statistics of multi-sequence alignments. We also compute the entropic cost, that is, the loss in entropy resulting from a constraint acting on the protein, such as the mutation of one particular amino-acid on a specific site, and relate this notion to the escape probability of the HIV virus. The case of lattice proteins, for which the entropy can be computed exactly, allows us to provide another illustration of the concept of cost, due to the competition of different folds. The relevance of the entropy in relation to directed evolution experiments is stressed.

  2. Carnot to Clausius: Caloric to Entropy

    ERIC Educational Resources Information Center

    Newburgh, Ronald

    2009-01-01

    This paper discusses how the Carnot engine led to the formulation of the second law of thermodynamics and entropy. The operation of the engine is analysed both in terms of heat as the caloric fluid and heat as a form of energy. A keystone of Carnot's thinking was the absolute conservation of caloric. Although the Carnot analysis was partly…

  3. Impact of Information Entropy on Teaching Effectiveness

    ERIC Educational Resources Information Center

    Wang, Zhi-guo

    2007-01-01

    Information entropy refers to the process in which information is sent out from the information source, transmitted through information channel and acquired by information sink, while the teaching process is the one of transmitting teaching information from teachers and teaching material to students. How to improve teaching effectiveness is…

  4. The Statistical Interpretation of Entropy: An Activity

    ERIC Educational Resources Information Center

    Timmberlake, Todd

    2010-01-01

    The second law of thermodynamics, which states that the entropy of an isolated macroscopic system can increase but will not decrease, is a cornerstone of modern physics. Ludwig Boltzmann argued that the second law arises from the motion of the atoms that compose the system. Boltzmann's statistical mechanics provides deep insight into the…

  5. Entropy of Mixing of Distinguishable Particles

    ERIC Educational Resources Information Center

    Kozliak, Evguenii I.

    2014-01-01

    The molar entropy of mixing yields values that depend only on the number of mixing components rather than on their chemical nature. To explain this phenomenon using the logic of chemistry, this article considers mixing of distinguishable particles, thus complementing the well-known approach developed for nondistinguishable particles, for example,…

  6. Symbolic transfer entropy: inferring directionality in biosignals.

    PubMed

    Staniek, Matthäus; Lehnertz, Klaus

    2009-12-01

    Inferring directional interactions from biosignals is of crucial importance to improve understanding of dynamical interdependences underlying various physiological and pathophysiological conditions. We here present symbolic transfer entropy as a robust measure to infer the direction of interactions between multidimensional dynamical systems. We demonstrate its performance in quantifying driver-responder relationships in a network of coupled nonlinear oscillators and in the human epileptic brain.

  7. Stock market stability: Diffusion entropy analysis

    NASA Astrophysics Data System (ADS)

    Li, Shouwei; Zhuang, Yangyang; He, Jianmin

    2016-05-01

    In this article, we propose a method to analyze the stock market stability based on diffusion entropy, and conduct an empirical analysis of Dow Jones Industrial Average. Empirical results show that this method can reflect the volatility and extreme cases of the stock market.

  8. Graphical representation of the excess entropy

    NASA Astrophysics Data System (ADS)

    Bednorz, Adam

    2001-09-01

    The generalized Mayer graphs invented by Nettleton and Green are used to express the probability distribution of statistical systems by reduced distribution functions. The entropy is expressed in terms of graphs and a simple rule of counting them is presented. The hyper-netted chain approximations are discussed.

  9. Tunnelling with a negative cosmological constant

    NASA Astrophysics Data System (ADS)

    Gibbons, G. W.

    1996-02-01

    The point of this paper is to see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the universe. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the 4-manifold. We raise the question of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its 3-volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.

  10. Thermodynamics of extremal rotating thin shells in an extremal BTZ spacetime and the extremal black hole entropy

    NASA Astrophysics Data System (ADS)

    Lemos, José P. S.; Minamitsuji, Masato; Zaslavskii, Oleg B.

    2017-02-01

    In a (2 +1 )-dimensional spacetime with a negative cosmological constant, the thermodynamics and the entropy of an extremal rotating thin shell, i.e., an extremal rotating ring, are investigated. The outer and inner regions with respect to the shell are taken to be the Bañados-Teitelbom-Zanelli (BTZ) spacetime and the vacuum ground state anti-de Sitter spacetime, respectively. By applying the first law of thermodynamics to the extremal thin shell, one shows that the entropy of the shell is an arbitrary well-behaved function of the gravitational area A+ alone, S =S (A+). When the thin shell approaches its own gravitational radius r+ and turns into an extremal rotating BTZ black hole, it is found that the entropy of the spacetime remains such a function of A+, both when the local temperature of the shell at the gravitational radius is zero and nonzero. It is thus vindicated by this analysis that extremal black holes, here extremal BTZ black holes, have different properties from the corresponding nonextremal black holes, which have a definite entropy, the Bekenstein-Hawking entropy S (A+)=A/+4G , where G is the gravitational constant. It is argued that for extremal black holes, in particular for extremal BTZ black holes, one should set 0 ≤S (A+)≤A/+4G;i.e., the extremal black hole entropy has values in between zero and the maximum Bekenstein-Hawking entropy A/+4 G . Thus, rather than having just two entropies for extremal black holes, as previous results have debated, namely, 0 and A/+4 G , it is shown here that extremal black holes, in particular extremal BTZ black holes, may have a continuous range of entropies, limited by precisely those two entropies. Surely, the entropy that a particular extremal black hole picks must depend on past processes, notably on how it was formed. A remarkable relation between the third law of thermodynamics and the impossibility for a massive body to reach the velocity of light is also found. In addition, in the procedure, it

  11. Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids.

    PubMed

    Dhabal, Debdas; Nguyen, Andrew Huy; Singh, Murari; Khatua, Prabir; Molinero, Valeria; Bandyopadhyay, Sanjoy; Chakravarty, Charusita

    2015-10-28

    Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW16). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW20), silicon (SW21), and water (SW(23.15) or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by S(trip), is also studied. S

  12. Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids

    NASA Astrophysics Data System (ADS)

    Dhabal, Debdas; Nguyen, Andrew Huy; Singh, Murari; Khatua, Prabir; Molinero, Valeria; Bandyopadhyay, Sanjoy; Chakravarty, Charusita

    2015-10-01

    Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW16). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW20), silicon (SW21), and water (SW23.15 or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by Strip, is also studied. Strip is a

  13. Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids

    SciTech Connect

    Dhabal, Debdas; Chakravarty, Charusita; Nguyen, Andrew Huy; Molinero, Valeria; Singh, Murari; Khatua, Prabir; Bandyopadhyay, Sanjoy

    2015-10-28

    Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW{sub 16}). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW{sub 20}), silicon (SW{sub 21}), and water (SW{sub 23.15} or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by S{sub trip

  14. National hospital input price index.

    PubMed

    Freeland, M S; Anderson, G; Schendler, C E

    1979-01-01

    The national community hospital input price index presented here isolates the effects of prices of goods and services required to produce hospital care and measures the average percent change in prices for a fixed market basket of hospital inputs. Using the methodology described in this article, weights for various expenditure categories were estimated and proxy price variables associated with each were selected. The index is calculated for the historical period 1970 through 1978 and forecast for 1979 through 1981. During the historical period, the input price index increased an average of 8.0 percent a year, compared with an average rate of increase of 6.6 percent for overall consumer prices. For the period 1979 through 1981, the average annual increase is forecast at between 8.5 and 9.0 per cent. Using the index to deflate growth in expenses, the level of real growth in expenditures per inpatient day (net service intensity growth) averaged 4.5 percent per year with considerable annual variation related to government and hospital industry policies.

  15. Hagedorn transition and topological entanglement entropy

    NASA Astrophysics Data System (ADS)

    Zuo, Fen; Gao, Yi-Hong

    2016-06-01

    Induced by the Hagedorn instability, weakly-coupled U (N) gauge theories on a compact manifold exhibit a confinement/deconfinement phase transition in the large-N limit. Recently we discover that the thermal entropy of a free theory on S3 gets reduced by a universal constant term, -N2 / 4, compared to that from completely deconfined colored states. This entropy deficit is due to the persistence of Gauss's law, and actually independent of the shape of the manifold. In this paper we show that this universal term can be identified as the topological entangle entropy both in the corresponding 4 + 1 D bulk theory and the dimensionally reduced theory. First, entanglement entropy in the bulk theory contains the so-called "particle" contribution on the entangling surface, which naturally gives rise to an area-law term. The topological term results from the Gauss's constraint of these surface states. Secondly, the high-temperature limit also defines a dimensionally reduced theory. We calculate the geometric entropy in the reduced theory explicitly, and find that it is given by the same constant term after subtracting the leading term of O (β-1). The two procedures are then applied to the confining phase, by extending the temperature to the complex plane. Generalizing the recently proposed 2D modular description to an arbitrary matter content, we show the leading local term is missing and no topological term could be definitely isolated. For the special case of N = 4 super Yang-Mills theory, the results obtained here are compared with that at strong coupling from the holographic derivation.

  16. Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

    NASA Astrophysics Data System (ADS)

    Shargel, Benjamin Hertz; Chou, Tom

    2009-10-01

    Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics.

  17. Emergent Geometry from Entropy and Causality

    NASA Astrophysics Data System (ADS)

    Engelhardt, Netta

    In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum

  18. Does the Lesche condition for stability validate generalized entropies?

    NASA Astrophysics Data System (ADS)

    Yamano, Takuya

    2004-08-01

    We reconsider the Lesche condition for a stability of entropies, which has been used for supporting validity of a generalized entropy over the others in recent papers. The fabric of an argument for applying the stability criterion with specific distributions to generalized entropies is shown to be interrogative. We show that a local stability analysis for the generalized entropies does not lead to the same conclusion as the one derived from the Lesche condition. It is also pointed out that the bound on the Shannon entropy by Lesche with an auxiliary function, and that on its generalized version are weak compared to those on the variational distance of their entropies against small changes in distribution. We conclude that there is no good reason for putting much emphasis on the criterion in the sense of Lesche when we advocate the validity of a generalized entropy.

  19. Minimal entropy probability paths between genome families.

    PubMed

    Ahlbrandt, Calvin; Benson, Gary; Casey, William

    2004-05-01

    We develop a metric for probability distributions with applications to biological sequence analysis. Our distance metric is obtained by minimizing a functional defined on the class of paths over probability measures on N categories. The underlying mathematical theory is connected to a constrained problem in the calculus of variations. The solution presented is a numerical solution, which approximates the true solution in a set of cases called rich paths where none of the components of the path is zero. The functional to be minimized is motivated by entropy considerations, reflecting the idea that nature might efficiently carry out mutations of genome sequences in such a way that the increase in entropy involved in transformation is as small as possible. We characterize sequences by frequency profiles or probability vectors, in the case of DNA where N is 4 and the components of the probability vector are the frequency of occurrence of each of the bases A, C, G and T. Given two probability vectors a and b, we define a distance function based as the infimum of path integrals of the entropy function H( p) over all admissible paths p(t), 0 < or = t< or =1, with p(t) a probability vector such that p(0)=a and p(1)=b. If the probability paths p(t) are parameterized as y(s) in terms of arc length s and the optimal path is smooth with arc length L, then smooth and "rich" optimal probability paths may be numerically estimated by a hybrid method of iterating Newton's method on solutions of a two point boundary value problem, with unknown distance L between the abscissas, for the Euler-Lagrange equations resulting from a multiplier rule for the constrained optimization problem together with linear regression to improve the arc length estimate L. Matlab code for these numerical methods is provided which works only for "rich" optimal probability vectors. These methods motivate a definition of an elementary distance function which is easier and faster to calculate, works on non

  20. Measuring capital market efficiency: long-term memory, fractal dimension and approximate entropy

    NASA Astrophysics Data System (ADS)

    Kristoufek, Ladislav; Vosvrda, Miloslav

    2014-07-01

    We utilize long-term memory, fractal dimension and approximate entropy as input variables for the Efficiency Index [L. Kristoufek, M. Vosvrda, Physica A 392, 184 (2013)]. This way, we are able to comment on stock market efficiency after controlling for different types of inefficiencies. Applying the methodology on 38 stock market indices across the world, we find that the most efficient markets are situated in the Eurozone (the Netherlands, France and Germany) and the least efficient ones in the Latin America (Venezuela and Chile).

  1. Nonexistence of equilibrium states at absolute negative temperatures

    NASA Astrophysics Data System (ADS)

    Romero-Rochín, Víctor

    2013-08-01

    We show that states of macroscopic systems with purported absolute negative temperatures are not stable under small, yet arbitrary, perturbations. We prove the previous statement using the fact that, in equilibrium, the entropy takes its maximum value. We discuss that, while Ramsey theoretical reformulation of the second law for systems with negative temperatures is logically correct, it must be a priori assumed that those states are in thermodynamic equilibrium. Since we argue that those states cannot occur, reversible processes are impossible, and, thus, Ramsey identification of absolute negative temperatures is untenable.

  2. Teaching Electrostatics and Entropy in Introductory Physics

    NASA Astrophysics Data System (ADS)

    Reeves, Mark

    Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology courses is important contribution of the entropy in driving fundamental biological processes towards equilibrium. I will present material developed to teach electrostatic screening in solutions and the function of nerve cells where entropic effects act to counterbalance electrostatic attraction. These ideas are taught in an introductory, calculus-based physics course to biomedical engineers using SCALEUP pedagogy. Results of student mastering of complex problems that cross disciplinary boundaries between biology and physics, as well as the challenges that they face in learning this material will be presented.

  3. Superior hydrogen storage in high entropy alloys.

    PubMed

    Sahlberg, Martin; Karlsson, Dennis; Zlotea, Claudia; Jansson, Ulf

    2016-11-10

    Metal hydrides (MHx) provide a promising solution for the requirement to store large amounts of hydrogen in a future hydrogen-based energy system. This requires the design of alloys which allow for a very high H/M ratio. Transition metal hydrides typically have a maximum H/M ratio of 2 and higher ratios can only be obtained in alloys based on rare-earth elements. In this study we demonstrate, for the first time to the best of our knowledge, that a high entropy alloy of TiVZrNbHf can absorb much higher amounts of hydrogen than its constituents and reach an H/M ratio of 2.5. We propose that the large hydrogen-storage capacity is due to the lattice strain in the alloy that makes it favourable to absorb hydrogen in both tetrahedral and octahedral interstitial sites. This observation suggests that high entropy alloys have future potential for use as hydrogen storage materials.

  4. Charged Renyi entropies for free scalar fields

    NASA Astrophysics Data System (ADS)

    Dowker, J. S.

    2017-04-01

    I first calculate the charged spherical Rényi entropy by a numerical method that does not require knowledge of any eigenvalue degeneracies, and applies to all odd dimensions. An image method is used to relate the full sphere values to those for an integer covering, n. It is shown to be equivalent to a ‘transformation’ property of the zeta-function. The n\\to ∞ limit is explicitly constructed analytically and a relation deduced between the limits of corner coefficients and the effective action (free energy) which generalises, for free fields, a result of Bueno, Myers and Witczak-Krempa and Elvang and Hadjiantonis to any dimension. Finally, the known polynomial expressions for the Rényi entropy on even spheres at zero chemical potential are re–derived in a different form and a simple formula for the conformal anomaly given purely in terms of central factorials is obtained.

  5. An investigation of combustion and entropy noise

    NASA Technical Reports Server (NTRS)

    Strahle, W. C.

    1977-01-01

    The relative importance of entropy and direct combustion noise in turbopropulsion systems and the parameters upon which these noise sources depend were studied. Theory and experiment were employed to determine that at least with the apparatus used here, entropy noise can dominate combustion noise if there is a sufficient pressure gradient terminating the combustor. Measurements included combustor interior fluctuating pressure, near and far field fluctuating pressure, and combustor exit plane fluctuating temperatures, as well as mean pressures and temperatures. Analysis techniques included spectral, cross-correlation, cross power spectra, and ordinary and partial coherence analysis. Also conducted were combustor liner modification experiments to investigate the origin of the frequency content of combustion noise. Techniques were developed to extract nonpropagational pseudo-sound and the heat release fluctuation spectra from the data.

  6. Thermodynamics of entropy-driven phase transformations.

    PubMed

    Radosz, A; Ostasiewicz, K; Magnuszewski, P; Damczyk, J; Radosiński, Ł; Kusmartsev, F V; Samson, J H; Mituś, A C; Pawlik, G

    2006-02-01

    Thermodynamic properties of one-dimensional lattice models exhibiting entropy-driven phase transformations are discussed in quantum and classical regimes. Motivated by the multistability of compounds exhibiting photoinduced phase transitions, we consider systems with asymmetric, double, and triple well on-site potential. One finds that among a variety of regimes, quantum versus classical, discrete versus continuum, a key feature is asymmetry distinguished as a "shift" type and "shape" type in limiting cases. The behavior of the specific heat indicates one phase transformation in a "shift" type and a sequence of two phase transformations in "shape"-type systems. Future analysis in higher dimensions should allow us to identify which of these entropy-driven phase transformations would evolve into phase transitions of the first order.

  7. New entropy formula with fluctuating reservoir

    NASA Astrophysics Data System (ADS)

    Biró, T. S.; Barnaföldi, G. G.; Ván, P.

    2015-01-01

    Finite heat reservoir capacity, C, and temperature fluctuation, ΔT / T, lead to modifications of the well known canonical exponential weight factor. Requiring that the corrections least depend on the one-particle energy, ω, we derive a deformed entropy, K(S) . The resultingformula contains the Boltzmann-Gibbs, Rényi, and Tsallis formulas as particular cases. For extreme large fluctuations, in the limit CΔT2 /T2 → ∞, a new parameter-free entropy-probability relation is gained. The corresponding canonical energy distribution is nearly Boltzmannian for high probability, but for low probability approaches the cumulative Gompertz distribution. The latter is met in several phenomena, like earthquakes, demography, tumor growth models, extreme value probability, etc.

  8. Superior hydrogen storage in high entropy alloys

    NASA Astrophysics Data System (ADS)

    Sahlberg, Martin; Karlsson, Dennis; Zlotea, Claudia; Jansson, Ulf

    2016-11-01

    Metal hydrides (MHx) provide a promising solution for the requirement to store large amounts of hydrogen in a future hydrogen-based energy system. This requires the design of alloys which allow for a very high H/M ratio. Transition metal hydrides typically have a maximum H/M ratio of 2 and higher ratios can only be obtained in alloys based on rare-earth elements. In this study we demonstrate, for the first time to the best of our knowledge, that a high entropy alloy of TiVZrNbHf can absorb much higher amounts of hydrogen than its constituents and reach an H/M ratio of 2.5. We propose that the large hydrogen-storage capacity is due to the lattice strain in the alloy that makes it favourable to absorb hydrogen in both tetrahedral and octahedral interstitial sites. This observation suggests that high entropy alloys have future potential for use as hydrogen storage materials.

  9. Gravitational surface Hamiltonian and entropy quantization

    NASA Astrophysics Data System (ADS)

    Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav

    2017-02-01

    The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.

  10. Hamiltonian formalism and path entropy maximization

    NASA Astrophysics Data System (ADS)

    Davis, Sergio; González, Diego

    2015-10-01

    Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the second law of thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the second law is a fundamental property of plausible inference.

  11. Multidimensional Scaling Visualization Using Parametric Entropy

    NASA Astrophysics Data System (ADS)

    Lopes, António M.; Tenreiro Machado, J. A.; Galhano, Alexandra M.

    2015-12-01

    This paper studies complex systems using a generalized multidimensional scaling (MDS) technique. Complex systems are characterized by time-series responses, interpreted as a manifestation of their dynamics. Two types of time-series are analyzed, namely 18 stock markets and the gross domestic product per capita of 18 countries. For constructing the MDS charts, indices based on parametric entropies are adopted. Multiparameter entropies allow the variation of the parameters leading to alternative sets of charts. The final MDS maps are then assembled by means of Procrustes’ method that maximizes the fit between the individual charts. Therefore, the proposed method can be interpreted as a generalization to higher dimensions of the standard technique that represents (and discretizes) items by means of single “points” (i.e. zero-dimensional “objects”). The MDS plots, involving one-, two- and three-dimensional “objects”, reveal a good performance in capturing the correlations between data.

  12. On the entropy function in sociotechnical systems

    PubMed Central

    Montroll, Elliott W.

    1981-01-01

    The entropy function H = -Σpj log pj (pj being the probability of a system being in state j) and its continuum analogue H = ∫p(x) log p(x) dx are fundamental in Shannon's theory of information transfer in communication systems. It is here shown that the discrete form of H also appears naturally in single-lane traffic flow theory. In merchandising, goods flow from a whole-saler through a retailer to a customer. Certain features of the process may be deduced from price distribution functions derived from Sears Roebuck and Company catalogues. It is found that the dispersion in logarithm of catalogue prices of a given year has remained about constant, independently of the year, for over 75 years. From this it may be inferred that the continuum entropy function for the variable logarithm of price had inadvertently, through Sears Roebuck policies, been maximized for that firm subject to the observed dispersion. PMID:16593136

  13. On the entropy function in sociotechnical systems.

    PubMed

    Montroll, E W

    1981-12-01

    The entropy function H = -Sigmap(j) log p(j) (p(j) being the probability of a system being in state j) and its continuum analogue H = integralp(x) log p(x) dx are fundamental in Shannon's theory of information transfer in communication systems. It is here shown that the discrete form of H also appears naturally in single-lane traffic flow theory. In merchandising, goods flow from a whole-saler through a retailer to a customer. Certain features of the process may be deduced from price distribution functions derived from Sears Roebuck and Company catalogues. It is found that the dispersion in logarithm of catalogue prices of a given year has remained about constant, independently of the year, for over 75 years. From this it may be inferred that the continuum entropy function for the variable logarithm of price had inadvertently, through Sears Roebuck policies, been maximized for that firm subject to the observed dispersion.

  14. Entropy analysis of substitutive sequences revisited

    NASA Astrophysics Data System (ADS)

    Karamanos, K.

    2001-11-01

    A given finite sequence of letters over a finite alphabet can always be algorithmically generated, in particular by a Turing machine. This fact is at the heart of complexity theory in the sense of Kolmogorov and Chaitin. A relevant question in this context is whether, given a statistically 'sufficiently long' sequence, there exists a deterministic finite automaton that generates it. In this paper we propose a simple criterion, based on measuring block entropies by lumping, which is satisfied by all automatic sequences. On the basis of this, one can determine that a given sequence is not automatic and obtain interesting information when the sequence is automatic. Following previous work on the Feigenbaum sequence, we give a necessary entropy-based condition valid for all automatic sequences read by lumping. Applications of these ideas to representative examples are discussed. In particular, we establish new entropic decimation schemes for the Thue-Morse, the Rudin-Shapiro and the paperfolding sequences read by lumping.

  15. Waveform information from quantum mechanical entropy

    NASA Astrophysics Data System (ADS)

    Funkhouser, Scott; Suski, William; Winn, Andrew

    2016-06-01

    Although the entropy of a given signal-type waveform is technically zero, it is nonetheless desirable to use entropic measures to quantify the associated information. Several such prescriptions have been advanced in the literature but none are generally successful. Here, we report that the Fourier-conjugated `total entropy' associated with quantum-mechanical probabilistic amplitude functions (PAFs) is a meaningful measure of information in non-probabilistic real waveforms, with either the waveform itself or its (normalized) analytic representation acting in the role of the PAF. Detailed numerical calculations are presented for both adaptations, showing the expected informatic behaviours in a variety of rudimentary scenarios. Particularly noteworthy are the sensitivity to the degree of randomness in a sequence of pulses and potential for detection of weak signals.

  16. The Increasingly Disordered History of Entropy

    NASA Astrophysics Data System (ADS)

    Rodriguez-Rosario, Cesar

    2008-03-01

    The interpretation of irreversibility had played a significant part of philosophical debates, but it was not until Carnot and his son established entropy as part of the empirical science of engines that the issue reached practical importance. It also had to wait for Maxwell, Boltzman, Gibbs and the birth of statistical mechanics that the concept of entropy was given a stronger theoretical basis, although the approximation it was based on is still a source of disagreement. This talk will focus on the debate from its early ``demonic'' times, past Szilard and Einstein building a refrigerator, to the role of von Neumann and Shannon in connecting the idea to information theory, without forgetting about the quantum mechanical master equations, all the way into its current use in quantum information theory.

  17. Efficient entropy coding for scalable video coding

    NASA Astrophysics Data System (ADS)

    Choi, Woong Il; Yang, Jungyoup; Jeon, Byeungwoo

    2005-10-01

    The standardization for the scalable extension of H.264 has called for additional functionality based on H.264 standard to support the combined spatio-temporal and SNR scalability. For the entropy coding of H.264 scalable extension, Context-based Adaptive Binary Arithmetic Coding (CABAC) scheme is considered so far. In this paper, we present a new context modeling scheme by using inter layer correlation between the syntax elements. As a result, it improves coding efficiency of entropy coding in H.264 scalable extension. In simulation results of applying the proposed scheme to encoding the syntax element mb_type, it is shown that improvement in coding efficiency of the proposed method is up to 16% in terms of bit saving due to estimation of more adequate probability model.

  18. Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys

    SciTech Connect

    Otto, Frederik; Yang, Ying; Bei, Hongbin; George, Easo P

    2013-01-01

    High configurational entropies have been hypothesized to stabilize solid solutions in equiatomic, multi-element alloys which have attracted much attention recently as high-entropy alloys with potentially interesting properties. To evaluate the usefulness of configurational entropy as a predictor of single-phase (solid solution) stability, we prepared five new equiatomic, quinary alloys by replacing individual elements one at a time in a CoCrFeMnNi alloy that was previously shown to be single-phase [1]. An implicit assumption here is that, if any one element is replaced by another, while keeping the total number of elements constant, the configurational entropy of the alloy is unchanged; therefore, the new alloys should also be single-phase. Additionally, the substitute elements that we chose, Ti for Co, Mo or V for Cr, V for Fe, and Cu for Ni, had the same room-temperature crystal structure and comparable size/electronegativity as the elements being replaced to maximize solid solubility consistent with the Hume-Rothery rules. For comparison, the base CoCrFeMnNi alloy was also prepared. After three-day anneals at elevated temperatures, multiple phases were observed in all but the base CoCrFeMnNi alloy suggesting that, by itself, configurational entropy is generally not able to override competing driving forces that also govern phase stability. Thermodynamic analyses were carried out for each of the constituent binaries in the investigated alloys (Co-Cr, Fe-Ni, Mo-Mn, etc,). Experimental results combined with the thermodynamic analyses suggest that, in general, enthalpy and non-configurational entropy have bigger influences on phase stability in equiatomic, multi-component alloys. Only when the alloy microstructure is a single-phase, approximately ideal solid solution does the contribution of configurational entropy to the total Gibbs free energy become dominant. Thus, high configurational entropy provides a way to rationalize, after the fact, why a solid solution

  19. Duality, entropy, and ADM mass in supergravity

    SciTech Connect

    Cerchiai, Bianca L.; Zumino, Bruno; Ferrara, Sergio; Marrani, Alessio

    2009-06-15

    We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property. Symmetries of both 'large' and 'small' extremal black holes are considered, as well as the ADM mass formula for N=4 and N=8 supergravity, preserving different fraction of supersymmetry. The interplay between BPS conditions and duality properties is an important aspect of this investigation.

  20. Entropy, recycling and macroeconomics of water resources

    NASA Astrophysics Data System (ADS)

    Karakatsanis, Georgios; Mamassis, Nikos; Koutsoyiannis, Demetris

    2014-05-01

    We propose a macroeconomic model for water quantity and quality supply multipliers derived by water recycling (Karakatsanis et al. 2013). Macroeconomic models that incorporate natural resource conservation have become increasingly important (European Commission et al. 2012). In addition, as an estimated 80% of globally used freshwater is not reused (United Nations 2012), under increasing population trends, water recycling becomes a solution of high priority. Recycling of water resources creates two major conservation effects: (1) conservation of water in reservoirs and aquifers and (2) conservation of ecosystem carrying capacity due to wastewater flux reduction. Statistical distribution properties of the recycling efficiencies -on both water quantity and quality- for each sector are of vital economic importance. Uncertainty and complexity of water reuse in sectors are statistically quantified by entropy. High entropy of recycling efficiency values signifies greater efficiency dispersion; which -in turn- may indicate the need for additional infrastructure for the statistical distribution's both shifting and concentration towards higher efficiencies that lead to higher supply multipliers. Keywords: Entropy, water recycling, water supply multipliers, conservation, recycling efficiencies, macroeconomics References 1. European Commission (EC), Food and Agriculture Organization (FAO), International Monetary Fund (IMF), Organization of Economic Cooperation and Development (OECD), United Nations (UN) and World Bank (2012), System of Environmental and Economic Accounting (SEEA) Central Framework (White cover publication), United Nations Statistics Division 2. Karakatsanis, G., N. Mamassis, D. Koutsoyiannis and A. Efstratiades (2013), Entropy and reliability of water use via a statistical approach of scarcity, 5th EGU Leonardo Conference - Hydrofractals 2013 - STAHY '13, Kos Island, Greece, European Geosciences Union, International Association of Hydrological Sciences

  1. The Tsallis entropy of natural information

    NASA Astrophysics Data System (ADS)

    Sneddon, Robert

    2007-12-01

    Estimating the information contained in natural data, such as electroencephalography data, is unusually difficult because the relationship between the physical data and the information that it encodes is unknown. This unknown relationship is often called the encoding problem. The present work provides a solution to this problem by deriving a method to estimate the Tsallis entropy in natural data. The method is based on two findings. The first finding is that the physical instantiation of any information event, that is, the physical occurrence of a symbol of information, must begin and end at a discontinuity or critical point (maximum, minimum, or saddle point) in the data. The second finding is that, in certain data types such as the encephalogram (EEG), the variance within of an EEG waveform event is directly proportional to its probability of occurrence. These two outcomes yield two results. The first is the easy binning of data into separate information events. The second is the ability to estimate probabilities in two ways: frequency counting and computing the variance within of an EEG waveform. These results are used to derive a linear estimator of the Tsallis entropy functional, allowing it to be estimated without deducing the encoding. This method for estimating the Tsallis entropy is first used to estimate the information in simple signals. The amount of information estimated is highly accurate. The method is then applied to two problems in electroencephalography. The first is distinguishing normal aging from very early Alzheimer's disease (mild cognitive impairment), and the second is medication monitoring of Alzheimer's disease treatment. The former is done with an accuracy of 92% and the latter with an accuracy of 91%. This detection accuracy is the highest published accuracy in the literature, which suggests that this method for Tsallis entropy estimation is both accurate and useful.

  2. Maximum entropy and Bayesian methods. Proceedings.

    NASA Astrophysics Data System (ADS)

    Grandy, W. T., Jr.; Schick, L. H.

    This volume contains a selection of papers presented at the Tenth Annual Workshop on Maximum Entropy and Bayesian Methods. The thirty-six papers included cover a wide range of applications in areas such as economics and econometrics, astronomy and astrophysics, general physics, complex systems, image reconstruction, and probability and mathematics. Together they give an excellent state-of-the-art overview of fundamental methods of data analysis.

  3. Bispectral index and spectral entropy in neuroanesthesia.

    PubMed

    Paolo Martorano, Pietro; Falzetti, Gabriele; Pelaia, Paolo

    2006-07-01

    Spectral Entropy (SpEn) is an alternative tool to the bispectral index (BIS) for monitoring depth of hypnosis. SpEn measures response entropy (RE) and state entropy (SE). This open-label prospective study was designed to evaluate SpEn and BIS in 20 patients undergoing elective supratentorial neurosurgery with craniotomy and resection of brain tumors. SpEn and BIS were obtained continuously by Datex Ohmeda M-entropy module S/5 (Helsinki, Finland) and Aspect Medical System BIS (Newton), respectively. Total intravenous anesthesia was performed in all patients by Fresenius Vial infusion system (Brezins, France) to maintain a plasma concentration of propofol of 2.5 to 5 microg mL(-1) and sufentanil of 0.2 to 0.4 etag mL(-1). SpEn, BIS, the estimated propofol effect-site concentrations (Ce), the mean arterial pressure (MAP), and the heart rate (HR) were recorded during 12 specific events: induction of anesthesia, patient stop counting, loss of blinking reflex, intubation, mayfield pinning, craniotomy, termination of propofol infusion, recovery of blinking reflex, coughing, limb movement, order execution, and extubation. Stated that prediction probability or P(K) represents an indicator probability to predict correctly the rank order of an arbitrary pair of distinct observed indices of depth of hypnosis (ie, clinical settings and SpEn indices, or BIS, Ce, MAP, HR), PK of BIS, SE, RE, and Ce provided a better depth of hypnosis than MAP and HR; RE being the best for rapidity, SE for sensitivity, and BIS for specificity. There is good correlation between the 3 hypnosis indices and Ce. This study demonstrates that SpEn provides a reproducible hypnosis index for patients undergoing supratentorial neurosurgical procedures.

  4. Duality, Entropy and ADM Mass in Supergravity

    SciTech Connect

    Cerchiai, Bianca L.; Ferrara, Sergio; Marrani, Alessio; Zumino, Bruno

    2009-02-23

    We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property. Symmetries of both"large" and"small" extremal black holes are considered, as well as the ADM mass formula for N=4 and N=8 supergravity, preserving different fraction of supersymmetry. The interplay between BPS conditions and duality properties is an important aspect of this investigation.

  5. Surface entropy of rare-gas clusters

    NASA Astrophysics Data System (ADS)

    Prasalovich, S.; Hansen, K.; Kjellberg, M.; Popok, V. N.; Campbell, E. E. B.

    2005-08-01

    Abundances of ArN+ and XeN+ clusters produced in a supersonic expansion source are inverted to find relative dissociation energies. The values around the shell and subshell closings at N =55, 71, and 147 differ from theoretical values derived from ground-state energies of Lennard-Jones clusters. A significant part of the difference can be accounted for by the conformational entropies of surface atoms and vacancies.

  6. Entropy Crises in Glasses and Random Heteropolymers.

    PubMed

    Wolynes, Peter G

    1997-01-01

    The concept of random first order transitions with configurational entropy crises provides a theoretical framework for understanding the glass transition. This paper discusses such transitions in exactly solvable spin glass models and in globular random heteropolymers and their relation to glass transitions in molecular fluids and polymers. The Vogel-Fulcher law is shown to be related to the search time through the energy landscape of an "entropic droplet."

  7. The Statistical Interpretation of Entropy: An Activity

    NASA Astrophysics Data System (ADS)

    Timmberlake, Todd

    2010-11-01

    The second law of thermodynamics, which states that the entropy of an isolated macroscopic system can increase but will not decrease, is a cornerstone of modern physics. Ludwig Boltzmann argued that the second law arises from the motion of the atoms that compose the system. Boltzmann's statistical mechanics provides deep insight into the functioning of the second law and also provided evidence for the existence of atoms at a time when many scientists (like Ernst Mach and Wilhelm Ostwald) were skeptical.

  8. Entropy Involved in Fidelity of DNA Replication

    PubMed Central

    Arias-Gonzalez, J. Ricardo

    2012-01-01

    Information has an entropic character which can be analyzed within the framework of the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is performed sufficiently slowly. Structural and recent single-molecule assays have provided dynamic details of polymerase machinery with insight into information processing. Here, we introduce a rigorous characterization of Shannon Information in biomolecular systems and apply it to DNA replication in the limit of no dissipation. Specifically, we devise an equilibrium pathway in DNA replication to determine the entropy generated in copying the information from a DNA template in the absence of friction. Both the initial state, the free nucleotides randomly distributed in certain concentrations, and the final state, a polymerized strand, are mesoscopic equilibrium states for the nucleotide distribution. We use empirical stacking free energies to calculate the probabilities of incorporation of the nucleotides. The copied strand is, to first order of approximation, a state of independent and non-indentically distributed random variables for which the nucleotide that is incorporated by the polymerase at each step is dictated by the template strand, and to second order of approximation, a state of non-uniformly distributed random variables with nearest-neighbor interactions for which the recognition of secondary structure by the polymerase in the resultant double-stranded polymer determines the entropy of the replicated strand. Two incorporation mechanisms arise naturally and their biological meanings are explained. It is known that replication occurs far from equilibrium and therefore the Shannon entropy here derived represents an upper bound for replication to take place. Likewise, this entropy sets a universal lower bound for the copying fidelity in replication. PMID:22912695

  9. Towards Accurate Microscopic Calculation of Solvation Entropies: Extending the Restraint Release Approach to Studies of Solvation Effects

    PubMed Central

    Singh, Nidhi; Warshel, Arieh

    2009-01-01

    The evaluation of the solvation entropies is a major conceptual and practical challenge. On the one hand, it is interesting to quantify the factors that are responsible for the solvation entropies in solutions, while on the other, it is essential to be able to assess the contributions of the solvation entropies to the binding free energies and related properties. In fact, the solvation entropies are neglected in almost all the studies of the binding entropies. The main problem is that widely used approaches, such as the quasiharmonic (QH) approximation do not provide reliable results particularly, in cases of shallow potential and multidimensional surfaces while brute force evaluations of the entropic effects by simulating temperature dependence of the free energy converges very slowly. This paper addresses the above issue by starting with an analysis of the factors that are responsible for the negative solvation entropy of ions, showing that it is not due to the change in the solvent vibration modes or to the solvent force constant but to the changes in the solvent configurational space upon change in the solute charges. We begin by clarifying that when one deals with aqueous solutions, it is easy to evaluate the corresponding entropic effect by the Langevin dipole(LD) treatment. However, in this work we are interested in developing a general microscopic tool that can be used to study similar effects in the proteins. To this end, we explore the ability of our restraint release (RR) approach to evaluate the solvation entropy. We start this analysis by reviewing the foundation of this approach and in particular, the requirements of minimizing the enthalpy contribution to the RR free energy. We then establish that our approach is not a specialized harmonic treatment but a rather powerful approach. Moving to the main topic of this work, we demonstrate that the RR approach provides quantitative results for the solvation entropies of monovalent and divalent ions and

  10. Nonequilibrium thermodynamics and maximum entropy production in the Earth system: applications and implications.

    PubMed

    Kleidon, Axel

    2009-06-01

    The Earth system is maintained in a unique state far from thermodynamic equilibrium, as, for instance, reflected in the high concentration of reactive oxygen in the atmosphere. The myriad of processes that transform energy, that result in the motion of mass in the atmosphere, in oceans, and on land, processes that drive the global water, carbon, and other biogeochemical cycles, all have in common that they are irreversible in their nature. Entropy production is a general consequence of these processes and measures their degree of irreversibility. The proposed principle of maximum entropy production (MEP) states that systems are driven to steady states in which they produce entropy at the maximum possible rate given the prevailing constraints. In this review, the basics of nonequilibrium thermodynamics are described, as well as how these apply to Earth system processes. Applications of the MEP principle are discussed, ranging from the strength of the atmospheric circulation, the hydrological cycle, and biogeochemical cycles to the role that life plays in these processes. Nonequilibrium thermodynamics and the MEP principle have potentially wide-ranging implications for our understanding of Earth system functioning, how it has evolved in the past, and why it is habitable. Entropy production allows us to quantify an objective direction of Earth system change (closer to vs further away from thermodynamic equilibrium, or, equivalently, towards a state of MEP). When a maximum in entropy production is reached, MEP implies that the Earth system reacts to perturbations primarily with negative feedbacks. In conclusion, this nonequilibrium thermodynamic view of the Earth system shows great promise to establish a holistic description of the Earth as one system. This perspective is likely to allow us to better understand and predict its function as one entity, how it has evolved in the past, and how it is modified by human activities in the future.

  11. Computational assessment of the entropy of solvation of small-sized hydrophobic entities.

    PubMed

    Mahajan, Reema; Kranzlmüller, Dieter; Volkert, Jens; Hansmann, Ulrich H E; Höfinger, Siegfried

    2006-12-21

    A high level polarizable force field is used to study the temperature dependence of hydrophobic hydration of small-sized molecules from computer simulations. Molecular dynamics (MD) simulations of liquid water at various temperatures form the basis of free energy perturbation calculations that consider the onset and growth of a repulsive sphere. This repulsive sphere acts as a model construct for the hydrophobic species. In the present study, an extension is pursued for seven independent target temperatures, ranging from close to the freezing point almost up to the boiling point of liquid water under standard conditions. Care is taken to maintain proper physico-chemical model descriptions by cross-checking with experimental water densities at the selected target temperatures. The polarizable force field description of molecular water turns out to be suitable throughout the entire temperature domain considered. Derivatives of the computed free energies of hydrophobic hydration with respect to the temperature give access to the changes in entropy. In practice the entropy differential is determined from the negative of the slope of tangential lines formed at a certain target temperature in the free energy profile. The obtained changes in entropy are negative for small-sized cavities, and hence reconfirm the basic ideas of the Lum-Chandler-Weeks theory on hydrophobic hydration of small-sized solutes.

  12. Multiscale permutation entropy analysis of electrocardiogram

    NASA Astrophysics Data System (ADS)

    Liu, Tiebing; Yao, Wenpo; Wu, Min; Shi, Zhaorong; Wang, Jun; Ning, Xinbao

    2017-04-01

    To make a comprehensive nonlinear analysis to ECG, multiscale permutation entropy (MPE) was applied to ECG characteristics extraction to make a comprehensive nonlinear analysis of ECG. Three kinds of ECG from PhysioNet database, congestive heart failure (CHF) patients, healthy young and elderly subjects, are applied in this paper. We set embedding dimension to 4 and adjust scale factor from 2 to 100 with a step size of 2, and compare MPE with multiscale entropy (MSE). As increase of scale factor, MPE complexity of the three ECG signals are showing first-decrease and last-increase trends. When scale factor is between 10 and 32, complexities of the three ECG had biggest difference, entropy of the elderly is 0.146 less than the CHF patients and 0.025 larger than the healthy young in average, in line with normal physiological characteristics. Test results showed that MPE can effectively apply in ECG nonlinear analysis, and can effectively distinguish different ECG signals.

  13. Understanding shape entropy through local dense packing

    PubMed Central

    van Anders, Greg; Klotsa, Daphne; Ahmed, N. Khalid; Engel, Michael; Glotzer, Sharon C.

    2014-01-01

    Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals was demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directional entropic forces (DEFs) that align neighboring particles, but these forces have been neither rigorously defined nor quantified in generic systems. Here, we show quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs. We define DEFs in generic systems and compute them for several hard particle systems. We show they are on the order of a few times the thermal energy (kBT) at the onset of ordering, placing DEFs on par with traditional depletion, van der Waals, and other intrinsic interactions. In experimental systems with these other interactions, we provide direct quantitative evidence that entropic effects of shape also contribute to self-assembly. We use DEFs to draw a distinction between self-assembly and packing behavior. We show that the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing. We show that this mechanism occurs in a wide class of systems and we treat, in a unified way, the entropy-driven phase behavior of arbitrary shapes, incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa. PMID:25344532

  14. Ensemble estimators for multivariate entropy estimation.

    PubMed

    Sricharan, Kumar; Wei, Dennis; Hero, Alfred O

    2013-07-01

    The problem of estimation of density functionals like entropy and mutual information has received much attention in the statistics and information theory communities. A large class of estimators of functionals of the probability density suffer from the curse of dimensionality, wherein the mean squared error (MSE) decays increasingly slowly as a function of the sample size T as the dimension d of the samples increases. In particular, the rate is often glacially slow of order O(T(-)(γ)(/)(d) ), where γ > 0 is a rate parameter. Examples of such estimators include kernel density estimators, k-nearest neighbor (k-NN) density estimators, k-NN entropy estimators, intrinsic dimension estimators and other examples. In this paper, we propose a weighted affine combination of an ensemble of such estimators, where optimal weights can be chosen such that the weighted estimator converges at a much faster dimension invariant rate of O(T(-1)). Furthermore, we show that these optimal weights can be determined by solving a convex optimization problem which can be performed offline and does not require training data. We illustrate the superior performance of our weighted estimator for two important applications: (i) estimating the Panter-Dite distortion-rate factor and (ii) estimating the Shannon entropy for testing the probability distribution of a random sample.

  15. Entropy Based Modelling for Estimating Demographic Trends.

    PubMed

    Li, Guoqi; Zhao, Daxuan; Xu, Yi; Kuo, Shyh-Hao; Xu, Hai-Yan; Hu, Nan; Zhao, Guangshe; Monterola, Christopher

    2015-01-01

    In this paper, an entropy-based method is proposed to forecast the demographical changes of countries. We formulate the estimation of future demographical profiles as a constrained optimization problem, anchored on the empirically validated assumption that the entropy of age distribution is increasing in time. The procedure of the proposed method involves three stages, namely: 1) Prediction of the age distribution of a country's population based on an "age-structured population model"; 2) Estimation the age distribution of each individual household size with an entropy-based formulation based on an "individual household size model"; and 3) Estimation the number of each household size based on a "total household size model". The last stage is achieved by projecting the age distribution of the country's population (obtained in stage 1) onto the age distributions of individual household sizes (obtained in stage 2). The effectiveness of the proposed method is demonstrated by feeding real world data, and it is general and versatile enough to be extended to other time dependent demographic variables.

  16. The concept of entropy in landscape evolution

    USGS Publications Warehouse

    Leopold, Luna Bergere; Langbein, Walter Basil

    1962-01-01

    The concept of entropy is expressed in terms of probability of various states. Entropy treats of the distribution of energy. The principle is introduced that the most probable condition exists when energy in a river system is as uniformly distributed as may be permitted by physical constraints. From these general considerations equations for the longitudinal profiles of rivers are derived that are mathematically comparable to those observed in the field. The most probable river profiles approach the condition in which the downstream rate of production of entropy per unit mass is constant. Hydraulic equations are insufficient to determine the velocity, depths, and slopes of rivers that are themselves authors of their own hydraulic geometries. A solution becomes possible by introducing the concept that the distribution of energy tends toward the most probable. This solution leads to a theoretical definition of the hydraulic geometry of river channels that agrees closely with field observations. The most probable state for certain physical systems can also be illustrated by random-walk models. Average longitudinal profiles and drainage networks were so derived and these have the properties implied by the theory. The drainage networks derived from random walks have some of the principal properties demonstrated by the Horton analysis; specifically, the logarithms of stream length and stream numbers are proportional to stream order.

  17. Information Flows? A Critique of Transfer Entropies

    NASA Astrophysics Data System (ADS)

    James, Ryan G.; Barnett, Nix; Crutchfield, James P.

    2016-06-01

    A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be dominated by the transfer entropy. Via straightforward examples, we show that it and a derivative quantity, the causation entropy, do not, in fact, quantify the flow of information. At one and the same time they can overestimate flow or underestimate influence. We isolate why this is the case and propose several avenues to alternate measures for information flow. We also address an auxiliary consequence: The proliferation of networks as a now-common theoretical model for large-scale systems, in concert with the use of transferlike entropies, has shoehorned dyadic relationships into our structural interpretation of the organization and behavior of complex systems. This interpretation thus fails to include the effects of polyadic dependencies. The net result is that much of the sophisticated organization of complex systems may go undetected.

  18. Entropy production in relativistic jet boundary layers

    NASA Astrophysics Data System (ADS)

    Kohler, Susanna; Begelman, Mitchell C.

    2015-01-01

    Hot relativistic jets, passing through a background medium with a pressure gradient p ∝ r-η where 2 < η ≤ 8/3, develop a shocked boundary layer containing a significant fraction of the jet power. In previous work, we developed a self-similar description of the boundary layer assuming isentropic flow, but we found that such models respect global energy conservation only for the special case η = 8/3. Here, we demonstrate that models with η < 8/3 can be made self-consistent if we relax the assumption of constant specific entropy. Instead, the entropy must increase with increasing r along the boundary layer, presumably due to multiple shocks driven into the flow as it gradually collimates. The increase in specific entropy slows the acceleration rate of the flow and provides a source of internal energy that could be channelled into radiation. We suggest that this process may be important for determining the radiative characteristics of tidal disruption events and gamma-ray bursts from collapsars.

  19. Understanding shape entropy through local dense packing

    DOE PAGES

    van Anders, Greg; Klotsa, Daphne; Ahmed, N. Khalid; ...

    2014-10-24

    Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals was demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directional entropic forces (DEFs) that align neighboring particles, but these forces have been neither rigorously defined nor quantified in generic systems. In this paper, we show quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs. We definemore » DEFs in generic systems and compute them for several hard particle systems. We show they are on the order of a few times the thermal energy (kBT) at the onset of ordering, placing DEFs on par with traditional depletion, van der Waals, and other intrinsic interactions. In experimental systems with these other interactions, we provide direct quantitative evidence that entropic effects of shape also contribute to self-assembly. We use DEFs to draw a distinction between self-assembly and packing behavior. We show that the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing. Finally, we show that this mechanism occurs in a wide class of systems and we treat, in a unified way, the entropy-driven phase behavior of arbitrary shapes, incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa.« less

  20. Understanding shape entropy through local dense packing

    SciTech Connect

    van Anders, Greg; Klotsa, Daphne; Ahmed, N. Khalid; Engel, Michael; Glotzer, Sharon C.

    2014-10-24

    Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals was demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directional entropic forces (DEFs) that align neighboring particles, but these forces have been neither rigorously defined nor quantified in generic systems. In this paper, we show quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs. We define DEFs in generic systems and compute them for several hard particle systems. We show they are on the order of a few times the thermal energy (kBT) at the onset of ordering, placing DEFs on par with traditional depletion, van der Waals, and other intrinsic interactions. In experimental systems with these other interactions, we provide direct quantitative evidence that entropic effects of shape also contribute to self-assembly. We use DEFs to draw a distinction between self-assembly and packing behavior. We show that the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing. Finally, we show that this mechanism occurs in a wide class of systems and we treat, in a unified way, the entropy-driven phase behavior of arbitrary shapes, incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa.

  1. Energy and Entropy Effects in Dissociation of Peptide Radical Anions

    SciTech Connect

    Laskin, Julia; Yang, Zhibo; Lam, Corey; Chu, Ivan K.

    2012-04-15

    Time- and collision energy-resolved surface-induced dissociation (SID) of peptide radical anions was studied for the first time using a Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR MS) configured for SID experiments. Peptide radical cations and anions were produced by gas-phase fragmentation of CoIII(salen)-peptide complexes. The effect of the charge, radical, and the presence of a basic residue on the energetics and dynamics of dissociation of peptide ions was examined using RVYIHPF (1) and HVYIHPF (2) as model systems. Comparison of the survival curves for of [M+H]{sup +}, [M-H]{sup -}, M{sup +{sm_bullet}}, and [M-2H]{sup -{sm_bullet}} ions of these precursors demonstrated that even-electron ions are more stable towards fragmentation than their odd-electron counterparts. RRKM modeling of the experimental data demonstrated that the lower stability of the positive radicals is mainly attributed to lower dissociation thresholds while entropy effects are responsible the relative instability of the negative radicals. Substitution of arginine with less basic histidine residue has a strong destabilizing effect on the [M+H]{sup +} ions and a measurable stabilizing effect on the odd-electron ions. Lower threshold energies for dissociation of both positive and negative radicals of 1 are attributed to the presence of lower-energy dissociation pathways that are most likely promoted by the presence of the basic residue.

  2. Irreversible Entropy Production in Two-Phase Mixing Layers

    NASA Technical Reports Server (NTRS)

    Okongo, Nora

    2003-01-01

    This report presents a study of dissipation (irreversible production of entropy) in three-dimensional, temporal mixing layers laden with evaporating liquid drops. The purpose of the study is to examine the effects of evaporating drops on the development of turbulent features in flows. Direct numerical simulations were performed to analyze transitional states of three mixing layers: one without drops, and two that included drops at different initial mass loadings. Without drops, the dissipation is essentially due to viscous effects. It was found that in the presence of drops, the largest contribution to dissipation was made by heating and evaporation of the drops, and that at large length scales, this contribution is positive (signifying that the drops reduce turbulence), while at small scales, this contribution is negative (the drops increase turbulence). The second largest contribution to dissipation was found to be associated with the chemical potential, which leads to an increase in turbulence at large scales and a decrease in turbulence at small scales. The next smaller contribution was found to be that of viscosity. The fact that viscosity effects are only third in order of magnitude in the dissipation is in sharp contrast to the situation for the mixing layer without the drops. The next smaller contribution - that of the drag and momentum of the vapor from the drops - was found to be negative at lower mass loading but to become positive at higher mass loading.

  3. Hand region extraction and gesture recognition from video stream with complex background through entropy analysis.

    PubMed

    Lee, JongShill; Lee, YoungJoo; Lee, EungHyuk; Hong, SeungHong

    2004-01-01

    Hand gesture recognition utilizing image processing relies upon recognition through markers or hand extraction by colors, and therefore is heavily restricted by the colors of clothes or skin. We propose a method to recognize band gestures extracted from images with a complex background for a more natural interface in HCI (human computer interaction). The proposed method obtains the image by subtracting one image from another sequential image, measures the entropy, separates hand region from images, tracks the hand region and recognizes hand gestures. Through entropy measurement, we have color information that has near distribution in complexion for regions that have big values and extracted hand region from input images. We could draw the hand region adaptively in variable lighting or individual differences because entropy offers color information as well as motion information at the same time. The detected contour using chain code for the hand region is extracted, and present centroidal profile method that is improved little more and recognized gesture of hand. In the experimental results for 6 kinds of hand gesture, it shows the recognition rate with more than 95% for person and 90-100% for each gesture at 5 frames/sec.

  4. Relations between work and entropy production for general information-driven, finite-state engines

    NASA Astrophysics Data System (ADS)

    Merhav, Neri

    2017-02-01

    We consider a system model of a general finite-state machine (ratchet) that simultaneously interacts with three kinds of reservoirs: a heat reservoir, a work reservoir, and an information reservoir, the latter being taken to be a running digital tape whose symbols interact sequentially with the machine. As has been shown in earlier work, this finite-state machine can act as a demon (with memory), which creates a net flow of energy from the heat reservoir into the work reservoir (thus extracting useful work) at the price of increasing the entropy of the information reservoir. Under very few assumptions, we propose a simple derivation of a family of inequalities that relate the work extraction with the entropy production. These inequalities can be seen as either upper bounds on the extractable work or as lower bounds on the entropy production, depending on the point of view. Many of these bounds are relatively easy to calculate and they are tight in the sense that equality can be approached arbitrarily closely. In their basic forms, these inequalities are applicable to any finite number of cycles (and not only asymptotically), and for a general input information sequence (possibly correlated), which is not necessarily assumed even stationary. Several known results are obtained as special cases.

  5. Steepest entropy ascent model for far-nonequilibrium thermodynamics: Unified implementation of the maximum entropy production principle

    NASA Astrophysics Data System (ADS)

    Beretta, Gian Paolo

    2014-10-01

    By suitable reformulations, we cast the mathematical frameworks of several well-known different approaches to the description of nonequilibrium dynamics into a unified formulation valid in all these contexts, which extends to such frameworks the concept of steepest entropy ascent (SEA) dynamics introduced by the present author in previous works on quantum thermodynamics. Actually, the present formulation constitutes a generalization also for the quantum thermodynamics framework. The analysis emphasizes that in the SEA modeling principle a key role is played by the geometrical metric with respect to which to measure the length of a trajectory in state space. In the near-thermodynamic-equilibrium limit, the metric tensor is directly related to the Onsager's generalized resistivity tensor. Therefore, through the identification of a suitable metric field which generalizes the Onsager generalized resistance to the arbitrarily far-nonequilibrium domain, most of the existing theories of nonequilibrium thermodynamics can be cast in such a way that the state exhibits the spontaneous tendency to evolve in state space along the path of SEA compatible with the conservation constraints and the boundary conditions. The resulting unified family of SEA dynamical models is intrinsically and strongly consistent with the second law of thermodynamics. The non-negativity of the entropy production is a general and readily proved feature of SEA dynamics. In several of the different approaches to nonequilibrium description we consider here, the SEA concept has not been investigated before. We believe it defines the precise meaning and the domain of general validity of the so-called maximum entropy production principle. Therefore, it is hoped that the present unifying approach may prove useful in providing a fresh basis for effective, thermodynamically consistent, numerical models and theoretical treatments of irreversible conservative relaxation towards equilibrium from far nonequilibrium

  6. Quasiparticle density of states by inversion with maximum entropy method

    NASA Astrophysics Data System (ADS)

    Sui, Xiao-Hong; Wang, Han-Ting; Tang, Hui; Su, Zhao-Bin

    2016-10-01

    We propose to extract the quasiparticle density of states (DOS) of the superconductor directly from the experimentally measured superconductor-insulator-superconductor junction tunneling data by applying the maximum entropy method to the nonlinear systems. It merits the advantage of model independence with minimum a priori assumptions. Various components of the proposed method have been carefully investigated, including the meaning of the targeting function, the mock function, as well as the role and the designation of the input parameters. The validity of the developed scheme is shown by two kinds of tests for systems with known DOS. As a preliminary application to a Bi2Sr2CaCu2O8 +δ sample with its critical temperature Tc=89 K , we extract the DOS from the measured intrinsic Josephson junction current data at temperatures of T =4.2 K , 45 K , 55 K , 95 K , and 130 K . The energy gap decreases with increasing temperature below Tc, while above Tc, a kind of energy gap survives, which provides an angle to investigate the pseudogap phenomenon in high-Tc superconductors. The developed method itself might be a useful tool for future applications in various fields.

  7. Canopy Research Network seeks input

    NASA Astrophysics Data System (ADS)

    In July 1993, the Canopy Research Network was established with a 2-year planning grant from the National Science Foundation to bring together forest canopy researchers, quantitative scientists, and computer specialists to establish methods for collecting, storing, analyzing, interpreting, and displaying three-dimensional data that relate to tree crowns and forest canopies. The CRN is now soliciting input from scientists in other fields who may have developed techniques and software to help obtain answers to questions that concern the complex three-dimensional structure of tree crowns and forest canopies. Over the next 3 years, the CRN plans to compile an array of research questions and issues requiring information on canopy structure, examine useful information models and software tools already in use in allied fields, and develop conceptual models and recommendations for the types and format of information and analyses necessary to answer research questions posed by canopy researchers.

  8. Unconventional entropy production in the presence of momentum-dependent forces

    NASA Astrophysics Data System (ADS)

    Kwon, Chulan; Yeo, Joonhyun; Lee, Hyun Keun; Park, Hyunggyu

    2016-03-01

    We investigate the unconventional nature of entropy production (EP) in nonequilibrium systems with odd-parity variables that change signs under time reversal. We consider the Brownian motion of a particle in contact with a heat reservoir, where the particle's momentum is an odd-parity variable. In the presence of an external momentum-dependent force, the EP transferred to the environment is found to be not equivalent to the usual reservoir entropy change due to heat transfer. An additional unconventional contribution to the EP, which is crucial for maintaining the non-negativity of the (average) total EP enforced by the second law of thermodynamics, appears. A few examples are considered to elucidate the novel nature of the EP. We also discuss detailed balance conditions with a momentum-dependent force.

  9. “Is Entropy conserved?” Student Understanding of Entropy in Introductory Physics

    NASA Astrophysics Data System (ADS)

    Christensen, Warren M.; Meltzer, D. E.

    2006-12-01

    As part of our continuing investigation into student learning of thermal physics in an introductory calculus-based course, we are probing student ideas regarding entropy and the second law of thermodynamics. We will present free-response and multiple-choice data collected both preand post-instruction from the previous five semesters. These data suggest that many key concepts are challenging for students. For example, as many as 75% of students, both before and after instruction, incorrectly claim that the total entropy of a system plus its surroundings must stay the same during a spontaneous process. Many of these students base their claim by asserting some sort of conservation principle for entropy. Early indications are that use of modified instruction with research-based materials may have yielded significant learning gains with some of these concepts. However, many student ideas remain resistant to change despite the modified instruction. *Supported in part by NSF DUE-9981140, PHY-0406724, and PHY-0604703

  10. “Is Entropy Conserved?” Student Understanding of Entropy in Introductory Physics

    NASA Astrophysics Data System (ADS)

    Christensen, Warren M.; Meltzer, D. E.

    2006-12-01

    As part of our continuing investigation into student learning of thermal physics in an introductory calculus-based course, we are probing student ideas regarding entropy and the second law of thermodynamics. We will present free-response and multiple-choice data collected both preand post-instruction from the previous five semesters. These data suggest that many key concepts are challenging for students. For example, as many as 75% of students, both before and after instruction, incorrectly claim that the total entropy of a system plus its surroundings must stay the same during a spontaneous process. Many of these students base their claim by asserting some sort of conservation principle for entropy. Early indications are that use of modified instruction with research-based materials may have yielded significant learning gains with some of these concepts. However, many student ideas remain resistant to change despite the modified instruction. *Supported in part by NSF DUE-9981140, PHY-0406724, and PHY-0604703

  11. Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential

    NASA Astrophysics Data System (ADS)

    Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.

    1995-08-01

    The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.

  12. A Larger Estimate of the Entropy of the Universe

    NASA Astrophysics Data System (ADS)

    Egan, Chas A.; Lineweaver, Charles H.

    2010-02-01

    Using recent measurements of the supermassive black hole (SMBH) mass function, we find that SMBHs are the largest contributor to the entropy of the observable universe, contributing at least an order of magnitude more entropy than previously estimated. The total entropy of the observable universe is correspondingly higher, and is S obs = 3.1+3.0 -1.7 × 10104 k. We calculate the entropy of the current cosmic event horizon to be S CEH = 2.6 ± 0.3 × 10122 k, dwarfing the entropy of its interior, S CEH int = 1.2+1.1 -0.7 × 10103 k. We make the first tentative estimate of the entropy of weakly interacting massive particle dark matter within the observable universe, S dm = 1088 ± 1 k. We highlight several caveats pertaining to these estimates and make recommendations for future work.

  13. Exploring stability of entropy analysis for signal with different trends

    NASA Astrophysics Data System (ADS)

    Zhang, Yin; Li, Jin; Wang, Jun

    2017-03-01

    Considering the effects of environment disturbances and instrument systems, the actual detecting signals always are carrying different trends, which result in that it is difficult to accurately catch signals complexity. So choosing steady and effective analysis methods is very important. In this paper, we applied entropy measures-the base-scale entropy and approximate entropy to analyze signal complexity, and studied the effect of trends on the ideal signal and the heart rate variability (HRV) signals, that is, linear, periodic, and power-law trends which are likely to occur in actual signals. The results show that approximate entropy is unsteady when we embed different trends into the signals, so it is not suitable to analyze signal with trends. However, the base-scale entropy has preferable stability and accuracy for signal with different trends. So the base-scale entropy is an effective method to analyze the actual signals.

  14. Left-right entanglement entropy of D p-branes

    NASA Astrophysics Data System (ADS)

    Zayas, Leopoldo A. Pando; Quiroz, Norma

    2016-11-01

    We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the left-moving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. We also consider Dp branes on compact dimensions and verify that the effects of T-duality act covariantly on the Dp brane entanglement entropy. We find that generically the left-right entanglement entropy provides a suitable generalization of boundary entropy and of the D-brane tension.

  15. ECG contamination of EEG signals: effect on entropy.

    PubMed

    Chakrabarti, Dhritiman; Bansal, Sonia

    2016-02-01

    Entropy™ is a proprietary algorithm which uses spectral entropy analysis of electroencephalographic (EEG) signals to produce indices which are used as a measure of depth of hypnosis. We describe a report of electrocardiographic (ECG) contamination of EEG signals leading to fluctuating erroneous Entropy values. An explanation is provided for mechanism behind this observation by describing the spread of ECG signals in head and neck and its influence on EEG/Entropy by correlating the observation with the published Entropy algorithm. While the Entropy algorithm has been well conceived, there are still instances in which it can produce erroneous values. Such erroneous values and their cause may be identified by close scrutiny of the EEG waveform if Entropy values seem out of sync with that expected at given anaesthetic levels.

  16. Generalized entropies and logarithms and their duality relations

    PubMed Central

    Hanel, Rudolf; Thurner, Stefan; Gell-Mann, Murray

    2012-01-01

    For statistical systems that violate one of the four Shannon–Khinchin axioms, entropy takes a more general form than the Boltzmann–Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with these generalized entropies, making them useful for understanding distribution functions of non-Markovian or nonergodic complex systems. For such systems where the composability axiom is violated there exist only two ways to implement the maximum entropy principle, one using escort probabilities, the other not. The two ways are connected through a duality. Here we show that this duality fixes a unique escort probability, which allows us to derive a complete theory of the generalized logarithms that naturally arise from the violation of this axiom. We then show how the functional forms of these generalized logarithms are related to the asymptotic scaling behavior of the entropy. PMID:23129618

  17. A family of generalized quantum entropies: definition and properties

    NASA Astrophysics Data System (ADS)

    Bosyk, G. M.; Zozor, S.; Holik, F.; Portesi, M.; Lamberti, P. W.

    2016-08-01

    We present a quantum version of the generalized (h,φ )-entropies, introduced by Salicrú et al. for the study of classical probability distributions. We establish their basic properties and show that already known quantum entropies such as von Neumann, and quantum versions of Rényi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicrú form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum (h,φ )-entropies under the action of quantum operations and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement and introduce a discussion on possible generalized conditional entropies as well.

  18. Fuzzy entropy based motion artifact detection and pulse rate estimation for fingertip photoplethysmography.

    PubMed

    Paradkar, Neeraj; Chowdhury, Shubhajit Roy

    2014-01-01

    The paper presents a fingertip photoplethysmography (PPG) based technique to estimate the pulse rate of the subject. The PPG signal obtained from a pulse oximeter is used for the analysis. The input samples are corrupted with motion artifacts due to minor motion of the subjects. Entropy measure of the input samples is used to detect the motion artifacts and estimate the pulse rate. A three step methodology is adapted to identify and classify signal peaks as true systolic peaks or artifact. CapnoBase database and CSL Benchmark database are used to analyze the technique and pulse rate estimation was performed with positive predictive value and sensitivity figures of 99.84% and 99.32% respectively for CapnoBase and 98.83% and 98.84% for CSL database respectively.

  19. On quantum Rényi entropies: A new generalization and some properties

    SciTech Connect

    Müller-Lennert, Martin; Dupuis, Frédéric; Szehr, Oleg; Fehr, Serge; Tomamichel, Marco

    2013-12-15

    The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.

  20. On Multiplying Negative Numbers.

    ERIC Educational Resources Information Center

    Crowley, Mary L.; Dunn, Kenneth A.

    1985-01-01

    Comments on the history of negative numbers, some methods that can be used to introduce the multiplication of negative numbers to students, and an explanation of why the product of two negative numbers is a positive number are included. (MNS)

  1. Detection of Floating Inputs in Logic Circuits

    NASA Technical Reports Server (NTRS)

    Cash, B.; Thornton, M. G.

    1984-01-01

    Simple modification of oscilloscope probe allows easy detection of floating inputs or tristate outputs in digital-IC's. Oscilloscope probe easily modified with 1/4 W resistor and switch for detecting floating inputs in CMOS logic circuits.

  2. Unusual Thermal Stability of High-Entropy Alloy Amorphous Structure

    DTIC Science & Technology

    2012-06-20

    1    REPORT Unusual Thermal Stability of High - Entropy Alloy Amorphous Structure Basic research for AOARD 114009 Award No. FA2386-11-1...stability of high - entropy alloy amorphous structure 5a. CONTRACT NUMBER FA23861114009 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Jien-Wei...at least 3 h. If substrate effect could be eliminated, the crystallization temperature would be higher. 15. SUBJECT TERMS high entropy alloys 16

  3. Efficient numerical methods for entropy-linear programming problems

    NASA Astrophysics Data System (ADS)

    Gasnikov, A. V.; Gasnikova, E. B.; Nesterov, Yu. E.; Chernov, A. V.

    2016-04-01

    Entropy-linear programming (ELP) problems arise in various applications. They are usually written as the maximization of entropy (minimization of minus entropy) under affine constraints. In this work, new numerical methods for solving ELP problems are proposed. Sharp estimates for the convergence rates of the proposed methods are established. The approach described applies to a broader class of minimization problems for strongly convex functionals with affine constraints.

  4. Proof of the entropy principle in Einstein-Maxwell theory

    NASA Astrophysics Data System (ADS)

    Gao, Sijie

    We consider a self-gravitating charged perfect fluid in a static spacetime. We assume that the Einstein constraint equation is satisfied. Then we prove that the extrema of the total entropy of fluid implies other components of Einstein's equation. Conversely, if Einstein's equation is satisfied, we show that the total entropy achieves an extremum. This work suggests that the maximum entropy principle is consistent with Einstein's equation when an electrostatic field is taken into account.

  5. Determining Dynamical Path Distributions usingMaximum Relative Entropy

    DTIC Science & Technology

    2015-05-31

    information. MaxCal is just The Principle of Maximum Entropy (MaxEnt) where constraints are changing in time. This simply amounts to an additional...Determining Dynamical Path Distributions using Maximum Relative Entropy The views, opinions and/or findings contained in this report are those of the...SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 Maximum Entropy

  6. Flight Test Validation of Optimal Input Design and Comparison to Conventional Inputs

    NASA Technical Reports Server (NTRS)

    Morelli, Eugene A.

    1997-01-01

    A technique for designing optimal inputs for aerodynamic parameter estimation was flight tested on the F-18 High Angle of Attack Research Vehicle (HARV). Model parameter accuracies calculated from flight test data were compared on an equal basis for optimal input designs and conventional inputs at the same flight condition. In spite of errors in the a priori input design models and distortions of the input form by the feedback control system, the optimal inputs increased estimated parameter accuracies compared to conventional 3-2-1-1 and doublet inputs. In addition, the tests using optimal input designs demonstrated enhanced design flexibility, allowing the optimal input design technique to use a larger input amplitude to achieve further increases in estimated parameter accuracy without departing from the desired flight test condition. This work validated the analysis used to develop the optimal input designs, and demonstrated the feasibility and practical utility of the optimal input design technique.

  7. Negative heat capacity in a left-handed system

    NASA Astrophysics Data System (ADS)

    Palma-Chilla, L.; Flores, J. C.

    2017-04-01

    This paper models a left-handed system by finite inductively interacting elements. To separate the internal energy a generic double spectral parametrization is proposed. The microcanonical formalism analytically allows to derive the entropy, temperature and heat capacity in each energy set. Particularly, the heat capacity was found to be negative at high energies. These analytical findings are supported through numerical results. Interestingly, numerically the heat capacity of the system seems to decline when increasing internal energy in both sets.

  8. Textual Enhancement of Input: Issues and Possibilities

    ERIC Educational Resources Information Center

    Han, ZhaoHong; Park, Eun Sung; Combs, Charles

    2008-01-01

    The input enhancement hypothesis proposed by Sharwood Smith (1991, 1993) has stimulated considerable research over the last 15 years. This article reviews the research on textual enhancement of input (TE), an area where the majority of input enhancement studies have aggregated. Methodological idiosyncrasies are the norm of this body of research.…

  9. Input Devices for Young Handicapped Children.

    ERIC Educational Resources Information Center

    Morris, Karen

    The versatility of the computer can be expanded considerably for young handicapped children by using input devices other than the typewriter-style keyboard. Input devices appropriate for young children can be classified into four categories: alternative keyboards, contact switches, speech input devices, and cursor control devices. Described are…

  10. Input filter compensation for switching regulators

    NASA Technical Reports Server (NTRS)

    Lee, F. C.

    1984-01-01

    Problems caused by input filter interaction and conventional input filter design techniques are discussed. The concept of feedforward control is modeled with an input filter and a buck regulator. Experimental measurement and comparison to the analytical predictions is carried out. Transient response and the use of a feedforward loop to stabilize the regulator system is described. Other possible applications for feedforward control are included.

  11. Entropy-based link prediction in weighted networks

    NASA Astrophysics Data System (ADS)

    Xu, Zhongqi; Pu, Cunlai; Ramiz Sharafat, Rajput; Li, Lunbo; Yang, Jian

    2017-01-01

    Information entropy has been proved to be an effective tool to quantify the structural importance of complex networks. In the previous work (Xu et al, 2016 \\cite{xu2016}), we measure the contribution of a path in link prediction with information entropy. In this paper, we further quantify the contribution of a path with both path entropy and path weight, and propose a weighted prediction index based on the contributions of paths, namely Weighted Path Entropy (WPE), to improve the prediction accuracy in weighted networks. Empirical experiments on six weighted real-world networks show that WPE achieves higher prediction accuracy than three typical weighted indices.

  12. Modeling the Overalternating Bias with an Asymmetric Entropy Measure

    PubMed Central

    Gronchi, Giorgio; Raglianti, Marco; Noventa, Stefano; Lazzeri, Alessandro; Guazzini, Andrea

    2016-01-01

    Psychological research has found that human perception of randomness is biased. In particular, people consistently show the overalternating bias: they rate binary sequences of symbols (such as Heads and Tails in coin flipping) with an excess of alternation as more random than prescribed by the normative criteria of Shannon's entropy. Within data mining for medical applications, Marcellin proposed an asymmetric measure of entropy that can be ideal to account for such bias and to quantify subjective randomness. We fitted Marcellin's entropy and Renyi's entropy (a generalized form of uncertainty measure comprising many different kinds of entropies) to experimental data found in the literature with the Differential Evolution algorithm. We observed a better fit for Marcellin's entropy compared to Renyi's entropy. The fitted asymmetric entropy measure also showed good predictive properties when applied to different datasets of randomness-related tasks. We concluded that Marcellin's entropy can be a parsimonious and effective measure of subjective randomness that can be useful in psychological research about randomness perception. PMID:27458418

  13. Non-convex entropies for conservation laws with involutions.

    PubMed

    Dafermos, Constantine M

    2013-12-28

    The paper discusses systems of conservation laws endowed with involutions and contingent entropies. Under the assumption that the contingent entropy function is convex merely in the direction of a cone in state space, associated with the involution, it is shown that the Cauchy problem is locally well posed in the class of classical solutions, and that classical solutions are unique and stable even within the broader class of weak solutions that satisfy an entropy inequality. This is on a par with the classical theory of solutions to hyperbolic systems of conservation laws endowed with a convex entropy. The equations of elastodynamics provide the prototypical example for the above setting.

  14. Generalized gravitational entropy of probe branes: flavor entanglement holographically

    NASA Astrophysics Data System (ADS)

    Karch, Andreas; Uhlemann, Christoph F.

    2014-05-01

    The notion of generalized gravitational entropy introduced by Lewkowycz and Maldacena allows, via the AdS/CFT correspondence, to calculate CFT entanglement entropies. We adapt the method to the case where flavor branes are present and treated in the probe approximation. This allows to calculate the leading flavor correction to the CFT entanglement entropy from the on-shell action of the probe, while dealing with the backreaction is avoided entirely and from the outset. As an application we give concise derivations for the contribution of massless and massive flavor degrees of freedom to the entanglement entropy in = 4 SYM theory.

  15. Generalized gravitational entropy of interacting scalar field and Maxwell field

    NASA Astrophysics Data System (ADS)

    Huang, Wung-Hong

    2014-12-01

    The generalized gravitational entropy proposed recently by Lewkowycz and Maldacena is extended to the interacting real scalar field and Maxwell field system. Using the BTZ geometry we first investigate the case of free real scalar field and then show a possible way to calculate the entropy of the interacting scalar field. Next, we investigate the Maxwell field system. We exactly solve the wave equation and calculate the analytic value of the generalized gravitational entropy. We also use the Einstein equation to find the effect of backreaction of the Maxwell field on the area of horizon. The associated modified area law is consistent with the generalized gravitational entropy.

  16. High-Order Entropy Stable Formulations for Computational Fluid Dynamics

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Fisher, Travis C.

    2013-01-01

    A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

  17. The information-theoretical entropy of some quantum oscillators

    SciTech Connect

    Popov, D. Pop, N.; Popov, M.

    2014-11-24

    The Wehrl entropy or the 'classical' entropy associated with a quantum system is the entropy of the probability distribution in phase space, corresponding to the Husimi Q-function in terms of coherent states. In the present paper, we shall focus our attention on the examination of the Wehrl entropy for both the pure and the mixed (thermal) states of the pseudoharmonic oscillator (PHO). The choice of the PHO is interesting because this oscillator is an intermediate between the ideal one-dimensional harmonic oscillator (HO-1D) and the more practical anharmonicone.

  18. Analysis of physiological signals using state space correlation entropy.

    PubMed

    Tripathy, Rajesh Kumar; Deb, Suman; Dandapat, Samarendra

    2017-02-01

    In this letter, the authors propose a new entropy measure for analysis of time series. This measure is termed as the state space correlation entropy (SSCE). The state space reconstruction is used to evaluate the embedding vectors of a time series. The SSCE is computed from the probability of the correlations of the embedding vectors. The performance of SSCE measure is evaluated using both synthetic and real valued signals. The experimental results reveal that, the proposed SSCE measure along with SVM classifier have sensitivity value of 91.60%, which is higher than the performance of both sample entropy and permutation entropy features for detection of shockable ventricular arrhythmia.

  19. Microscopic diagonal entropy and its connection to basic thermodynamic relations

    SciTech Connect

    Polkovnikov, Anatoli

    2011-02-15

    We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as S{sub d}=-{Sigma}{sub n{rho}nn}ln{rho}{sub nn} with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the conventional von Neumann entropy S{sub n} = -Tr{rho} ln {rho}. However, in contrast to S{sub n}, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. We also show that the d-entropy can be expressed through the energy distribution function and thus it is measurable, at least in principle. Under very generic assumptions of the locality of the Hamiltonian and non-integrability the d-entropy becomes a unique function of the average energy in large systems and automatically satisfies the fundamental thermodynamic relation. This relation reduces to the first law of thermodynamics for quasi-static processes. The d-entropy is also automatically conserved for adiabatic processes. We illustrate our results with explicit examples and show that S{sub d} behaves consistently with expectations from thermodynamics.

  20. First law of entanglement entropy in topologically massive gravity

    NASA Astrophysics Data System (ADS)

    Cheng, Long; Hung, Ling-Yan; Liu, Si-Nong; Zhou, Hong-Zhe

    2016-09-01

    In this paper we explore the validity of the first law of entanglement entropy in the context of topologically massive gravity (TMG). We find that the variation of the holographic entanglement entropy under perturbation from the pure anti-de Sitter background satisfies the first law upon imposing the bulk equations of motion in a given time slice, despite the appearance of instabilities in the bulk for generic gravitational Chern-Simons coupling μ . The Noether-Wald entropy is different from the holographic entanglement entropy in a general boosted frame. However, this discrepancy does not affect the entanglement first law.

  1. Biogenic inputs to ocean mixing.

    PubMed

    Katija, Kakani

    2012-03-15

    Recent studies have evoked heated debate about whether biologically generated (or biogenic) fluid disturbances affect mixing in the ocean. Estimates of biogenic inputs have shown that their contribution to ocean mixing is of the same order as winds and tides. Although these estimates are intriguing, further study using theoretical, numerical and experimental techniques is required to obtain conclusive evidence of biogenic mixing in the ocean. Biogenic ocean mixing is a complex problem that requires detailed understanding of: (1) marine organism behavior and characteristics (i.e. swimming dynamics, abundance and migratory behavior), (2) mechanisms utilized by swimming animals that have the ability to mix stratified fluids (i.e. turbulence and fluid drift) and (3) knowledge of the physical environment to isolate contributions of marine organisms from other sources of mixing. In addition to summarizing prior work addressing the points above, observations on the effect of animal swimming mode and body morphology on biogenic fluid transport will also be presented. It is argued that to inform the debate on whether biogenic mixing can contribute to ocean mixing, our studies should focus on diel vertical migrators that traverse stratified waters of the upper pycnocline. Based on our understanding of mixing mechanisms, body morphologies, swimming modes and body orientation, combined with our knowledge of vertically migrating populations of animals, it is likely that copepods, krill and some species of gelatinous zooplankton and fish have the potential to be strong sources of biogenic mixing.

  2. Multi-variable control of chaos using PSO-based minimum entropy control

    NASA Astrophysics Data System (ADS)

    Sadeghpour, Mehdi; Salarieh, Hassan; Vossoughi, Gholamreza; Alasty, Aria

    2011-06-01

    The minimum entropy (ME) control is a chaos control technique which causes chaotic behavior to vanish by stabilizing unstable periodic orbits of the system without using mathematical model of the system. In this technique some controller type, normally delayed feedback controller, with an adjustable parameter such as feedback gain is used. The adjustable parameter is determined such that the entropy of the system is minimized. Proposed in this paper is the PSO-based multi-variable ME control. In this technique two or more control parameters are adjusted concurrently either in a single or in multiple control inputs. Thus it is possible to use two or more feedback terms in the delayed feedback controller and adjust their gains. Also the multi-variable ME control can be used in multi-input systems. The minimizing engine in this technique is the particle swarm optimizer. Using online PSO, the PSO-based multi-variable ME control technique is applied to stabilize the 1-cycle fixed points of the Logistic map, the Hénon map, and the chaotic Duffing system. The results exhibit good effectiveness and performance of this controller.

  3. Negative Ions in Space.

    PubMed

    Millar, Thomas J; Walsh, Catherine; Field, Thomas A

    2017-02-08

    Until a decade ago, the only anion observed to play a prominent role in astrophysics was H(-). The bound-free transitions in H(-) dominate the visible opacity in stars with photospheric temperatures less than 7000 K, including the Sun. The H(-) anion is also believed to have been critical to the formation of molecular hydrogen in the very early evolution of the Universe. Once H2 formed, about 500 000 years after the Big Bang, the expanding gas was able to lose internal gravitational energy and collapse to form stellar objects and "protogalaxies", allowing the creation of heavier elements such as C, N, and O through nucleosynthesis. Although astronomers had considered some processes through which anions might form in interstellar clouds and circumstellar envelopes, including the important role that polycyclic aromatic hydrocarbons might play in this, it was the detection in 2006 of rotational line emission from C6H(-) that galvanized a systematic study of the abundance, distribution, and chemistry of anions in the interstellar medium. In 2007, the Cassini mission reported the unexpected detection of anions with mass-to-charge ratios of up to ∼10 000 in the upper atmosphere of Titan; this observation likewise instigated the study of fundamental chemical processes involving negative ions among planetary scientists. In this article, we review the observations of anions in interstellar clouds, circumstellar envelopes, Titan, and cometary comae. We then discuss a number of processes by which anions can be created and destroyed in these environments. The derivation of accurate rate coefficients for these processes is an essential input for the chemical kinetic modeling that is necessary to fully extract physics from the observational data. We discuss such models, along with their successes and failings, and finish with an outlook on the future.

  4. Information Entropy of Influenza A Segment 7

    NASA Astrophysics Data System (ADS)

    Thompson, William A.; Fan, Shaohua; Weltman, Joel K.

    2008-12-01

    Information entropy (H) is a measure of uncertainty at each position within in a sequence of nucleotides.H was used to characterize a set of influenza A segment 7 nucleotide sequences. Nucleotide locations of high entropy were identified near the 5’ start of all of the sequences and the sequences were assigned to subsets according to synonymous nucleotide variants at those positions: either uracil at position six (U6), cytosine at position six (C6), adenine (A12) at position 12, guanine at position 12 (G12), adenine at position 15 (A15) or cytosine (C15) at position 15. H values were found to be correlated/corresponding (Kendall tau) along the lengths of the nucleotide segments of the subset pairs at each position. However, the H values of each subset of sequences were statistically distinguishable from those of the other member of the pair (Kolmogorov-Smirnov test). The joint probability of uncorrelated distributions of U6 and C6 sequences to viral subtypes and to viral host species was 34 times greater than for the A12:G12 subset pair and 214 times greater than for the A15:C15 pair. This result indicates that the high entropy position six of segment 7 is either a reporter or a sentinel location. The fact that not one of the H5N1 sequences in the dataset was a member of the C6 subset, but all 125 H5N1 sequences are members of the U6 subset suggests a non-random sentinel function.

  5. Algorithms for the Markov entropy decomposition

    NASA Astrophysics Data System (ADS)

    Ferris, Andrew J.; Poulin, David

    2013-05-01

    The Markov entropy decomposition (MED) is a recently proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps of the MED, principally solving a minimization problem with a preconditioned Newton's algorithm, as well as how to extract global susceptibilities and thermal responses. We demonstrate the power of the method with the spin-1/2 XXZ model on the 2D square lattice, including the extraction of critical points and details of each phase. Although the method shares some qualitative similarities with exact diagonalization, we show that the MED is both more accurate and significantly more flexible.

  6. Entropy production fluctuations of finite Markov chains

    NASA Astrophysics Data System (ADS)

    Jiang, Da-Quan; Qian, Min; Zhang, Fu-Xi

    2003-09-01

    For almost every trajectory segment over a finite time span of a finite Markov chain with any given initial distribution, the logarithm of the ratio of its probability to that of its time-reversal converges exponentially to the entropy production rate of the Markov chain. The large deviation rate function has a symmetry of Gallavotti-Cohen type, which is called the fluctuation theorem. Moreover, similar symmetries also hold for the rate functions of the joint distributions of general observables and the logarithmic probability ratio.

  7. Fuzzy geometry, entropy, and image information

    NASA Technical Reports Server (NTRS)

    Pal, Sankar K.

    1991-01-01

    Presented here are various uncertainty measures arising from grayness ambiguity and spatial ambiguity in an image, and their possible applications as image information measures. Definitions are given of an image in the light of fuzzy set theory, and of information measures and tools relevant for processing/analysis e.g., fuzzy geometrical properties, correlation, bound functions and entropy measures. Also given is a formulation of algorithms along with management of uncertainties for segmentation and object extraction, and edge detection. The output obtained here is both fuzzy and nonfuzzy. Ambiguity in evaluation and assessment of membership function are also described.

  8. Entropy driven patterning in vibrofluidized granular materials

    NASA Astrophysics Data System (ADS)

    Galanis, Jennifer

    2008-10-01

    We investigate pattern formation in vertically vibrofluidized rod and sphere granular mixtures confined to quasi-2D containers. In a pure rod system, crowding induces an isotropic-to-nematic phase transition. The inclusion of spheres destabilizes both the isotropic and nematic states. Instead, small independent rod bundles form, where the long axes of rods are closely approximated. To investigate the role of entropy maximization in the granular experiments, we performed strict-2D equilibrium Monte Carlo simulations of hard rods and spheres and found analogous patterning. Similarities and differences between the steady state experiments and equilibrium simulations will be discussed. In collaboration with Daniel Harries, The Hebrew University of Jerusalem.

  9. Thermodynamic Entropy as a Noether Invariant.

    PubMed

    Sasa, Shin-Ichi; Yokokura, Yuki

    2016-04-08

    We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal nonuniform time translation t→t+ηℏβ, where η is a small parameter, ℏ is the Planck constant, β is the inverse temperature that depends on the energy and control parameter, and trajectories in the phase space are restricted to those consistent with quasistatic processes in thermodynamics.

  10. Thermodynamic Entropy as a Noether Invariant

    NASA Astrophysics Data System (ADS)

    Sasa, Shin-ichi; Yokokura, Yuki

    2016-04-01

    We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal nonuniform time translation t →t +η ℏβ , where η is a small parameter, ℏ is the Planck constant, β is the inverse temperature that depends on the energy and control parameter, and trajectories in the phase space are restricted to those consistent with quasistatic processes in thermodynamics.

  11. Dynamical maximum entropy approach to flocking

    NASA Astrophysics Data System (ADS)

    Cavagna, Andrea; Giardina, Irene; Ginelli, Francesco; Mora, Thierry; Piovani, Duccio; Tavarone, Raffaele; Walczak, Aleksandra M.

    2014-04-01

    We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy model distribution consistent with temporal and spatial correlations of flight direction. When bird neighborhoods evolve rapidly, this dynamical inference correctly learns the parameters of the model, while a static one relying only on the spatial correlations fails. When neighbors change slowly and the detailed balance is satisfied, we recover the static procedure. We demonstrate the validity of the method on simulated data. The approach is applicable to other systems of active matter.

  12. Temporal Correlations and Neural Spike Train Entropy

    SciTech Connect

    Schultz, Simon R.; Panzeri, Stefano

    2001-06-18

    Sampling considerations limit the experimental conditions under which information theoretic analyses of neurophysiological data yield reliable results. We develop a procedure for computing the full temporal entropy and information of ensembles of neural spike trains, which performs reliably for limited samples of data. This approach also yields insight to the role of correlations between spikes in temporal coding mechanisms. The method, when applied to recordings from complex cells of the monkey primary visual cortex, results in lower rms error information estimates in comparison to a {open_quotes}brute force{close_quotes} approach.

  13. Spectral entropy in monitoring anesthetic depth.

    PubMed

    Escontrela Rodríguez, B; Gago Martínez, A; Merino Julián, I; Martínez Ruiz, A

    2016-10-01

    Monitoring the brain response to hypnotics in general anesthesia, with the nociceptive and hemodynamic stimulus interaction, has been a subject of intense investigation for many years. Nowadays, monitors of depth of anesthesia are based in processed electroencephalogram by different algorithms, some of them unknown, to obtain a simplified numeric parameter approximate to brain activity state in each moment. In this review we evaluate if spectral entropy suitably reflects the brain electric behavior in response to hypnotics and the different intensity nociceptive stimulus effect during a surgical procedure.

  14. Quantum entropy production in phase space

    NASA Astrophysics Data System (ADS)

    Deffner, Sebastian

    2014-03-01

    A fluctuation theorem for the nonequilibrium entropy production in quantum phase space is derived, which enables the consistent thermodynamic description of arbitrary quantum systems, open and closed. The new treatment naturally generalizes classical results to the quantum domain. As an illustration the harmonic oscillator dragged through a thermal bath is solved numerically. Finally, the significance of the new approach is discussed in detail, and the phase space treatment is opposed to the two time energy measurement approach. We acknowledge financial support by a fellowship within the postdoc-program of the German Academic Exchange Service (DAAD, contract No D/11/40955) and from the National Science Foundation (USA) under grant DMR-1206971.

  15. Maximum entropy and Bayesian methods. Proceedings.

    NASA Astrophysics Data System (ADS)

    Fougère, P. F.

    Bayesian probability theory and maximum entropy are the twin foundations of consistent inductive reasoning about the physical world. This volume contains thirty-two papers which are devoted to both foundations and applications and combine tutorial presentations and more research oriented contributions. Together these provide a state of the art account of latest developments in such diverse areas as coherent imaging, regression analysis, tomography, neural networks, plasma theory, quantum mechanics, and others. The methods described will be of great interest to mathematicians, physicists, astronomers, crystallographers, engineers and those involved in all aspects of signal processing.

  16. Entropy of 4D extremal black holes

    NASA Astrophysics Data System (ADS)

    Johnson, Clifford V.; Khuri, Ramzi R.; Myers, Robert C.

    1996-02-01

    We derive the Bekenstein-Hawking entropy formula for four-dimensional Reissner-Nordström extremal black holes in type II string theory. The derivation is performed in two separate (T-dual) weak coupling pictures. One uses a type IIB bound state problem of D5- and D1-branes, while the other uses a bound state problem of D0- and D4-branes with macroscopic fundamental type IIA strings. In both cases, the D-brane systems are also bound to a Kaluza-Klein monopole, which then yields the four-dimensional black hole at strong coupling.

  17. A generalized model on the evaluation of entropy and entropy of mixing of liquid Na-Sn alloys

    NASA Astrophysics Data System (ADS)

    Satpathy, Alok; Sengupta, Saumendu

    2017-01-01

    Recently proposed theory of entropy of mixing of the structurally inhomogeneous binary liquid alloys of alkali metals and group-IV elements is applied successfully to the liquid Na-Sn alloy. This alloy indicates chemical short range ordering (CSRO) i.e. exhibits partially salt like characteristics due to strong tendencies to compound formation, in the solid as well as in the liquid state. So, the generalized model for entropy of charged-hard-spheres mixture of arbitrary charge and size is employed to evaluate entropies of mixing, treating the sample as partially charge transfer system. The computed entropies of mixing are in excellent agreement with the experimental data.

  18. PREVIMER : Meteorological inputs and outputs

    NASA Astrophysics Data System (ADS)

    Ravenel, H.; Lecornu, F.; Kerléguer, L.

    2009-09-01

    PREVIMER is a pre-operational system aiming to provide a wide range of users, from private individuals to professionals, with short-term forecasts about the coastal environment along the French coastlines bordering the English Channel, the Atlantic Ocean, and the Mediterranean Sea. Observation data and digital modelling tools first provide 48-hour (probably 96-hour by summer 2009) forecasts of sea states, currents, sea water levels and temperatures. The follow-up of an increasing number of biological parameters will, in time, complete this overview of coastal environment. Working in partnership with the French Naval Hydrographic and Oceanographic Service (Service Hydrographique et Océanographique de la Marine, SHOM), the French National Weather Service (Météo-France), the French public science and technology research institute (Institut de Recherche pour le Développement, IRD), the European Institute of Marine Studies (Institut Universitaire Européen de la Mer, IUEM) and many others, IFREMER (the French public institute fo marine research) is supplying the technologies needed to ensure this pertinent information, available daily on Internet at http://www.previmer.org, and stored at the Operational Coastal Oceanographic Data Centre. Since 2006, PREVIMER publishes the results of demonstrators assigned to limited geographic areas and to specific applications. This system remains experimental. The following topics are covered : Hydrodynamic circulation, sea states, follow-up of passive tracers, conservative or non-conservative (specifically of microbiological origin), biogeochemical state, primary production. Lastly, PREVIMER provides researchers and R&D departments with modelling tools and access to the database, in which the observation data and the modelling results are stored, to undertake environmental studies on new sites. The communication will focus on meteorological inputs to and outputs from PREVIMER. It will draw the lessons from almost 3 years during

  19. Turn customer input into innovation.

    PubMed

    Ulwick, Anthony W

    2002-01-01

    It's difficult to find a company these days that doesn't strive to be customer-driven. Too bad, then, that most companies go about the process of listening to customers all wrong--so wrong, in fact, that they undermine innovation and, ultimately, the bottom line. What usually happens is this: Companies ask their customers what they want. Customers offer solutions in the form of products or services. Companies then deliver these tangibles, and customers just don't buy. The reason is simple--customers aren't expert or informed enough to come up with solutions. That's what your R&D team is for. Rather, customers should be asked only for outcomes--what they want a new product or service to do for them. The form the solutions take should be up to you, and you alone. Using Cordis Corporation as an example, this article describes, in fine detail, a series of effective steps for capturing, analyzing, and utilizing customer input. First come indepth interviews, in which a moderator works with customers to deconstruct a process or activity in order to unearth "desired outcomes." Addressing participants' comments one at a time, the moderator rephrases them to be both unambiguous and measurable. Once the interviews are complete, researchers then compile a comprehensive list of outcomes that participants rank in order of importance and degree to which they are satisfied by existing products. Finally, using a simple mathematical formula called the "opportunity calculation," researchers can learn the relative attractiveness of key opportunity areas. These data can be used to uncover opportunities for product development, to properly segment markets, and to conduct competitive analysis.

  20. Statistical optimization for passive scalar transport: maximum entropy production versus maximum Kolmogorov-Sinai entropy

    NASA Astrophysics Data System (ADS)

    Mihelich, M.; Faranda, D.; Dubrulle, B.; Paillard, D.

    2015-03-01

    We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov-Sinai entropy for a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov-Sinai entropy, seen as functions of a parameter f connected to the jump probability, admit a unique maximum denoted fmaxEP and fmaxKS. The behaviour of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this paper is that fmaxEP and fmaxKS have the same Taylor expansion at first order in the deviation from equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP(N) tends towards a non-zero value, while fmaxKS(N) tends to 0 when N goes to infinity. For values of N typical of those adopted by Paltridge and climatologists working on maximum entropy production (N ≍ 10-100), we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N* such that fmaxEP and fmaxKS coincide, at least up to a second-order parameter proportional to the non-equilibrium fluxes imposed to the boundaries. We find that the optimal resolution N* depends on the non-equilibrium fluxes, so that deeper convection should be represented on finer grids. This result points to the inadequacy of using a single grid for representing convection in climate and weather models. Moreover, the application of this principle to passive scalar transport parametrization is therefore expected to provide both the value of the optimal flux, and of the optimal number of degrees of freedom (resolution) to describe the system.

  1. Entropy and information causality in general probabilistic theories

    NASA Astrophysics Data System (ADS)

    Barnum, Howard; Barrett, Jonathan; Orloff Clark, Lisa; Leifer, Matthew; Spekkens, Robert; Stepanik, Nicholas; Wilce, Alex; Wilke, Robin

    2010-03-01

    We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu-Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.

  2. Using heteroclinic orbits to quantify topological entropy in fluid flows

    NASA Astrophysics Data System (ADS)

    Sattari, Sulimon; Chen, Qianting; Mitchell, Kevin A.

    2016-03-01

    Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or "ghost," rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding of ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.

  3. Evaluating the uncertainty of input quantities in measurement models

    NASA Astrophysics Data System (ADS)

    Possolo, Antonio; Elster, Clemens

    2014-06-01

    uncertainty propagation exercises. In this we deviate markedly and emphatically from the GUM Supplement 1, which gives pride of place to the Principle of Maximum Entropy as a means to assign probability distributions to input quantities.

  4. What is the vortex ``transport entropy"?

    NASA Astrophysics Data System (ADS)

    Sergeev, Andrei; Reizer, Michael; Mitin, Vladimir

    2008-03-01

    Below the superconducting transition the large thermomagnetic effects in the type II superconductors are determined by magnetic vortices. These topological excitations are completely different from particle-hole exctitations in the Fermi liquid and, therefore, the thermomagnetic effects do not require particle-hole asymmetry. Thermomagnetic effects in the vortex state are widely described in terms of the ``transport entropy.'' Despite of intensive theoretical and experimental investigations, this mysterious quantity is still in conflict with either the Onsager principle or the third law of thermodynamics [1]. We resolve this forty years enigma taking into account the magnetization current in the presence of the temperature gradient. Then contributions of superconducting currents of vortices are canceled in the Nernst effect, and, therefore, in agreement with the Onsager relation, both the Nernst and Ettingshausen phenomena originate solely from vortex cores. Finally, the transport entropy turns out to be by a factor of 4 ln (λ/ ξ) smaller than that used in literature [1] (λ is the magnetic field penetration depth, ξ is the coherence length. For high-temperature cuprates this factor is ˜20. [1] R.P. Huebener, Magnetic flux structures in superconductors, Springer-Verlag, Berlin, (1979).

  5. Braid Entropy of Two-Dimensional Turbulence

    PubMed Central

    Francois, Nicolas; Xia, Hua; Punzmann, Horst; Faber, Benjamin; Shats, Michael

    2015-01-01

    The evolving shape of material fluid lines in a flow underlies the quantitative prediction of the dissipation and material transport in many industrial and natural processes. However, collecting quantitative data on this dynamics remains an experimental challenge in particular in turbulent flows. Indeed the deformation of a fluid line, induced by its successive stretching and folding, can be difficult to determine because such description ultimately relies on often inaccessible multi-particle information. Here we report laboratory measurements in two-dimensional turbulence that offer an alternative topological viewpoint on this issue. This approach characterizes the dynamics of a braid of Lagrangian trajectories through a global measure of their entanglement. The topological length of material fluid lines can be derived from these braids. This length is found to grow exponentially with time, giving access to the braid topological entropy . The entropy increases as the square root of the turbulent kinetic energy and is directly related to the single-particle dispersion coefficient. At long times, the probability distribution of is positively skewed and shows strong exponential tails. Our results suggest that may serve as a measure of the irreversibility of turbulence based on minimal principles and sparse Lagrangian data. PMID:26689261

  6. Adaptable recursive binary entropy coding technique

    NASA Astrophysics Data System (ADS)

    Kiely, Aaron B.; Klimesh, Matthew A.

    2002-07-01

    We present a novel data compression technique, called recursive interleaved entropy coding, that is based on recursive interleaving of variable-to variable length binary source codes. A compression module implementing this technique has the same functionality as arithmetic coding and can be used as the engine in various data compression algorithms. The encoder compresses a bit sequence by recursively encoding groups of bits that have similar estimated statistics, ordering the output in a way that is suited to the decoder. As a result, the decoder has low complexity. The encoding process for our technique is adaptable in that each bit to be encoded has an associated probability-of-zero estimate that may depend on previously encoded bits; this adaptability allows more effective compression. Recursive interleaved entropy coding may have advantages over arithmetic coding, including most notably the admission of a simple and fast decoder. Much variation is possible in the choice of component codes and in the interleaving structure, yielding coder designs of varying complexity and compression efficiency; coder designs that achieve arbitrarily small redundancy can be produced. We discuss coder design and performance estimation methods. We present practical encoding and decoding algorithms, as well as measured performance results.

  7. Measuring the entropy from shifted boundary conditions

    NASA Astrophysics Data System (ADS)

    Giusti, L.; Pepe, M.

    We explore a new computational strategy for determining the equation of state of the SU(3) Yang-Mills theory. By imposing shifted boundary conditions, the entropy density is computed from the vacuum expectation value of the off-diagonal components T_{0k} of the energy-momentum tensor. A step-scaling function is introduced to span a wide range in temperature values. We present preliminary numerical results for the entropy density and its step-scaling function obtained at eight temperature values in the range T_c - 15 T_c. At each temperature, discretization effects are removed by simulating the theory at several lattice spacings and by extrapolating the results to the continuum limit. Finite-size effects are always kept below the statistical errors. The absence of ultraviolet power divergences and the remarkably small discretization effects allow for a precise determination of the step-scaling function in the explored temperature range. These findings establish this strategy as a viable solution for an accurate determination of the equation of state in a wide range of temperature values.

  8. Entropy measures of collective cell migration

    NASA Astrophysics Data System (ADS)

    Whitby, Ariadne; Parrinello, Simona; Faisal, Aldo

    2015-03-01

    Collective cell migration is a critical process during tissue formation and repair. To this end there is a need to develop tools to quantitatively measure the dynamics of collective cell migration obtained from microscopy data. Drawing on statistical physics we use entropy of velocity fields derived from dense optic flow to quantitatively measure collective migration. Using peripheral nerve repair after injury as experimental system, we study how Schwann cells, guided by fibroblasts, migrate in cord-like structures across the cut, paving a highway for neurons. This process of emergence of organised behaviour is key for successful repair, yet the emergence of leader cells and transition from a random to ordered state is not understood. We find fibroblasts induce correlated directionality in migrating Schwann cells as measured by a decrease in the entropy of motion vector. We show our method is robust with respect to image resolution in time and space, giving a principled assessment of how various molecular mechanisms affect macroscopic features of collective cell migration. Finally, the generality of our method allows us to process both simulated cell movement and microscopic data, enabling principled fitting and comparison of in silico to in vitro. ICCS, Imperial College London & MRC Clinical Sciences Centre.

  9. Direct measurements of the magnetic entropy change.

    PubMed

    Nielsen, K K; Bez, H N; von Moos, L; Bjørk, R; Eriksen, D; Bahl, C R H

    2015-10-01

    An experimental device that can accurately measure the magnetic entropy change, Δs, as a function of temperature, T, and magnetic field, H, is presented. The magnetic field source is in this case a set of counter-rotating concentric Halbach-type magnets, which produce a highly homogeneous applied field with constant orientation. The field may be varied from 0 to 1.5 T in a continuous way. The temperature stability of the system is controlled to within ±10 mK and the standard range for the current setup is from 230 K to 330 K. The device is under high vacuum and we show that thermal losses to the ambient are negligible in terms of the calorimetric determination of the magnetic entropy change, while the losses cannot be ignored when correcting for the actual sample temperature. We apply the device to two different types of samples; one is commercial grade Gd, i.e., a pure second-order phase transition material, while the other is Gd5Si2Ge2, a first order magnetic phase transition material. We demonstrate the device's ability to fully capture the thermal hysteresis of the latter sample by following appropriate thermal resetting scheme and magnetic resetting scheme.

  10. RELAP-7 Numerical Stabilization: Entropy Viscosity Method

    SciTech Connect

    R. A. Berry; M. O. Delchini; J. Ragusa

    2014-06-01

    The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.

  11. Superior hydrogen storage in high entropy alloys

    PubMed Central

    Sahlberg, Martin; Karlsson, Dennis; Zlotea, Claudia; Jansson, Ulf

    2016-01-01

    Metal hydrides (MHx) provide a promising solution for the requirement to store large amounts of hydrogen in a future hydrogen-based energy system. This requires the design of alloys which allow for a very high H/M ratio. Transition metal hydrides typically have a maximum H/M ratio of 2 and higher ratios can only be obtained in alloys based on rare-earth elements. In this study we demonstrate, for the first time to the best of our knowledge, that a high entropy alloy of TiVZrNbHf can absorb much higher amounts of hydrogen than its constituents and reach an H/M ratio of 2.5. We propose that the large hydrogen-storage capacity is due to the lattice strain in the alloy that makes it favourable to absorb hydrogen in both tetrahedral and octahedral interstitial sites. This observation suggests that high entropy alloys have future potential for use as hydrogen storage materials. PMID:27829659

  12. Entropy-based consistent model driven architecture

    NASA Astrophysics Data System (ADS)

    Niepostyn, Stanisław Jerzy

    2016-09-01

    A description of software architecture is a plan of the IT system construction, therefore any architecture gaps affect the overall success of an entire project. The definitions mostly describe software architecture as a set of views which are mutually unrelated, hence potentially inconsistent. Software architecture completeness is also often described in an ambiguous way. As a result most methods of IT systems building comprise many gaps and ambiguities, thus presenting obstacles for software building automation. In this article the consistency and completeness of software architecture are mathematically defined based on calculation of entropy of the architecture description. Following this approach, in this paper we also propose our method of automatic verification of consistency and completeness of the software architecture development method presented in our previous article as Consistent Model Driven Architecture (CMDA). The proposed FBS (Functionality-Behaviour-Structure) entropy-based metric applied in our CMDA approach enables IT architects to decide whether the modelling process is complete and consistent. With this metric, software architects could assess the readiness of undergoing modelling work for the start of IT system building. It even allows them to assess objectively whether the designed software architecture of the IT system could be implemented at all. The overall benefit of such an approach is that it facilitates the preparation of complete and consistent software architecture more effectively as well as it enables assessing and monitoring of the ongoing modelling development status. We demonstrate this with a few industry examples of IT system designs.

  13. Caloric restriction, metabolic rate, and entropy.

    PubMed

    Demetrius, Lloyd

    2004-09-01

    Caloric restriction increases life span in many types of animals. This article proposes a mechanism for this effect based on the hypothesis that metabolic stability, the capacity of an organism to maintain steady state values of redox couples, is a prime determinant of longevity. We integrate the stability-longevity hypothesis with a molecular model of metabolic activity (quantum metabolism), and an entropic theory of evolutionary change (directionality theory), to propose a proximate mechanism and an evolutionary rationale for aging. The mechanistic features of the new theory of aging are invoked to predict that caloric restriction extends life span by increasing metabolic stability. The evolutionary model is exploited to predict that the large increases in life span under caloric restriction observed in rats, a species with early sexual maturity, narrow reproductive span and large litter size, and hence low entropy, will not hold for primates. We affirm that in the case of humans, a species with late sexual maturity, broad reproductive span and small litter size, and hence high entropy, the response of life span to caloric restriction will be negligible.

  14. Quasiclassical coarse graining and thermodynamic entropy

    SciTech Connect

    Gell-Mann, Murray; Hartle, James B.

    2007-08-15

    Our everyday descriptions of the universe are highly coarse grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited powers of observation and computation. But in the modern quantum mechanics of closed systems, some measure of coarse graining is inescapable because there are no nontrivial, probabilistic, fine-grained descriptions. This essay explores the consequences of that fact. Quantum theory allows for various coarse-grained descriptions, some of which are mutually incompatible. For most purposes, however, we are interested in the small subset of 'quasiclassical descriptions' defined by ranges of values of averages over small volumes of densities of conserved quantities such as energy and momentum and approximately conserved quantities such as baryon number. The near-conservation of these quasiclassical quantities results in approximate decoherence, predictability, and local equilibrium, leading to closed sets of equations of motion. In any description, information is sacrificed through the coarse graining that yields decoherence and gives rise to probabilities for histories. In quasiclassical descriptions, further information is sacrificed in exhibiting the emergent regularities summarized by classical equations of motion. An appropriate entropy measures the loss of information. For a 'quasiclassical realm' this is connected with the usual thermodynamic entropy as obtained from statistical mechanics. It was low for the initial state of our universe and has been increasing since.

  15. Technology in the high entropy world.

    PubMed

    Tambo, N

    2006-01-01

    Modern growing society is mainly driven by oils and may be designated "petroleum civilisation". However, the basic energy used to drive the global ecosystem is solar radiation. The amount of fossil energy consumption is minimal in the whole global energy balance. Economic growth is mainly controlled by the fossil (commercial) energy consumption rate in urban areas. Water and sanitation systems are bridging economical activities and global ecosystems. Therefore, vast amounts of high entropy solar energy should always be taken into account in the water industry. Only in urban/industrial areas where most of the GDP is earned, are commercial energy driven systems inevitably introduced with maximum effort for energy saving. A water district concept to ensure appropriate quality use with the least deterioration of the environment is proposed. In other areas, decentralised water and sanitation systems driven on soft energy paths would be recommended. A process and system designed on a high entropy energy system would be the foundation for a future urban metabolic system revolution for when oil-based energy become scarce.

  16. Multiscale entropy analysis of biological signals

    NASA Astrophysics Data System (ADS)

    Costa, Madalena; Goldberger, Ary L.; Peng, C.-K.

    2005-02-01

    Traditional approaches to measuring the complexity of biological signals fail to account for the multiple time scales inherent in such time series. These algorithms have yielded contradictory findings when applied to real-world datasets obtained in health and disease states. We describe in detail the basis and implementation of the multiscale entropy (MSE) method. We extend and elaborate previous findings showing its applicability to the fluctuations of the human heartbeat under physiologic and pathologic conditions. The method consistently indicates a loss of complexity with aging, with an erratic cardiac arrhythmia (atrial fibrillation), and with a life-threatening syndrome (congestive heart failure). Further, these different conditions have distinct MSE curve profiles, suggesting diagnostic uses. The results support a general “complexity-loss” theory of aging and disease. We also apply the method to the analysis of coding and noncoding DNA sequences and find that the latter have higher multiscale entropy, consistent with the emerging view that so-called “junk DNA” sequences contain important biological information.

  17. Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys.

    PubMed

    Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K

    2016-07-20

    The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.

  18. Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys

    NASA Astrophysics Data System (ADS)

    Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.

    2016-07-01

    The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.

  19. Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys

    PubMed Central

    Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.

    2016-01-01

    The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk. PMID:27435922

  20. Self-similar random process and chaotic behavior in serrated flow of high entropy alloys

    DOE PAGES

    Chen, Shuying; Yu, Liping; Ren, Jingli; ...

    2016-07-20

    Here, the statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and theremore » is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.« less